# discrete math

Most popular questions-
## discrete math

list five integers that are congruent to 4 modulo 12 4, 16, 36, ... any integer of the from n*12 + 4 where n=0, 1, 2, 3...

*asked by thisha on November 6, 2006* -
## Discrete Math

A bag contains 5 red marbles, 4 yellow marbles, 3 green marbles, 2 orange marbles and 2 purple marbles. If three marbles are removed, what is the probability that at least one of them is red?

*asked by Steven on January 19, 2014* -
## discrete math

How many strings of four decimal digits (Note there are 10 possible digits and a string can be of the form 0014 etc., i.e., can start with zeros.) (a) have exactly three digits which are 9s?

*asked by carlton on April 3, 2012* -
## Discrete Math

In roulette, a wheel with 38 numbers is spun. Of these, 18 are red, 18 are black, and 2 are green. The probability that when the wheel is spun it lands on any particular number is 1/38. a) What is the probability that the wheel lands on a red number? b)

*asked by Christopher on October 29, 2016* -
## discrete math

Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties: (a) are divisible by 5 and by 7. (b) have distinct digits. (c) are not divisible by either 5 or 7.

*asked by carlton on April 8, 2012* -
## discrete math

prove that if n is an integer and 3n+2 is even, then n is even using a)a proof by contraposition b)a proof by contradiction I'll try part b, you'll have to refresh me on what contraposition means here. Here is the claim we start with If n is an integer and

*asked by audryana on September 27, 2006* -
## Discrete Math

Prove that a function f : A -> B is one to one if and only if any non-empty subset S ⊆ A, f^-1 (f(S)) = S. DO NOT assume a priori that the inverse function f^-1 exists; in this question f^-1 (S) denotes the pre-image of S.

*asked by AAAAAAAAAAA on November 4, 2019* -
## Discrete Math

How many friends must you have to guarantee that at least five of them will have birthdays in the same month?

*asked by Chris on October 11, 2013* -
## discrete math

if you have 5 signal flags and can send messages by hoisting 1 or more flags on a flagpole, how many messages can you send? please help!!

*asked by kennedy on September 15, 2008* -
## discrete math

let d be a positive integer. Show that among any group of d+19not necessarily consecutive) integers there are two with exactly the same remainder when they are divided by d. The possible values of the remainders are 0, 1, 2, ...d-1. So there are a total of

*asked by thisha on November 29, 2006* -
## discrete math

convert(BADFACED)16 FROM ITS HEXADECIMAL EXPANION TO ITS BINARY EXPANSION i think you have to convert BAdFACED *16 then the BIanary something.. okay i really don't get this sorry!! ** 3 men and 6 women are applying for several jobs. The jobs are book

*asked by thisha on November 6, 2006* -
## Discrete Math

A factory makes automobile parts. Each part has a code consisting of a letter and three digits, such as C117, O076, or Z920. Last week the factory made 60,000 parts. Prove that there are at least three parts that have the same serial number.

*asked by Francesca on April 20, 2011* -
## Discrete Math

Using the ordinary alphabet and allowing repeated letters, find the number of words of length 8 that have exactly one B. How do I solve this? Please leave an explanation to solve this.

*asked by Adedeji Ogunba on November 18, 2018* -
## discrete math

Consider the graph given above. Add an edge so the resulting graph has an Euler circuit (without repeating an existing edge). Now give an Euler circuit through the graph with this new edge by listing the vertices in the order visited.

*asked by carlton on May 6, 2012* -
## Discrete Math

Each Student at a certain university is given a 6-digit code (such as 123789 or 001122) (a) how many different codes are there? (b) how many codes read the same forward and backward? (c) how many codes contain only odd digits? (d) how many codes contain at

*asked by Raff on December 10, 2014* -
## Discrete Math

With 50 pennies in three jars labeled A, B and C, how may ways can you put the pennies in the jars assuming they are identical with at least two pennies in each jar?

*asked by Samantha on October 27, 2011* -
## discrete math

1)prove that if x is rational and x not equal to 0, then 1/x is rational. 2) prove that there is a positive integers that equals the sum of the positive integers not exceeding it. Is your proof constructive or nonconstructive? For 1) use the definition of

*asked by thisha on September 28, 2006* -
## Discrete Math

I am really stuck on these problems. I've worked a lot of them but I can't get these. Sometimes I think I know the answer but I can't show how I got it. 1.) Solve each matrix equation for X. 2X + 5A = B 2.) Find the following matrices: a. AB b. BA A= 2 4 3

*asked by Ryan on February 25, 2010* -
## Discrete Math

Theorem: For every integer n, if x and y are positive integers with max(x, y) = n, then x = y. Basic Step: Suppose that n = 1. If max(x, y) = 1 and x and y are positive integers, we have x = 1 and y = 1. Inductive Step: Let k be a positive integer. Assume

*asked by Francesca on March 25, 2011* -
## Discrete Math

A box contains 55 balls numbered from 1 to 55. If 8 balls are drawn with replacement, what is the probability that at least two of them have the same number?

*asked by Nick on April 27, 2011* -
## Discrete Math

Consider the following relations on R, the set of real numbers a. R1: x, y ∈ R if and only if x = y. b. R2: x, y ∈ R if and only if x ≥ y. c. R3 : x, y ∈ R if and only if xy < 0. Determine whether or not each relation is flexible, symmetric,

*asked by Laurey on February 7, 2011* -
## Discrete Math

A special type of password consists of four different letters of the alphabet, where each letter is used only once. How many different possible passwords are there?

*asked by John on June 30, 2013* -
## Discrete Math

Find z so that 5% of the area under the standard normal curve lies to the right of z. the answer according to the book is 1.645, anyone got any ideas on how to get this?

*asked by Jessica on January 21, 2013* -
## DISCRETE MATH

We have a relation R on Z+ defined as follows: mRn if and only if m|n. a. Explain why the relation R is not a function. b. Determine the set A = {m ∈ Z|mR52} and give its cardinality |A|. c. Determine the set B = {n ∈ Z|52Rn}. d. Indicate whether A ∩

*asked by Anonymous on May 31, 2015* -
## Discrete Math

I know how to apply Euclidean algorithm when a is greater then b, but I'm not quite sure what to do when b is greater than a. For example a = 111 and b = 201. How do I solve this? Is it possible?

*asked by Ch00 on February 28, 2011* -
## Discrete Math

( 0,0,0,1 0,0,1,0 1,1,0,1 1,1,1,0) How would I draw the adj matrices if i cannot connect c and a and d and b?

*asked by Adedeji Ogunba on November 25, 2018* -
## discrete math

You have borrowed $8000 from the bank. Suppose you want to repay a fixed amount of money for each of the following n years (except possibly the last year), and the annual interest rate r does not change in these n years. For example, if r = 10% and you

*asked by akash on April 30, 2017* -
## Discrete Math

(2) Suppose A is the set of students currently registered at the University of Calgary, B is the set of professors at the University of Calgary, and C is the set of courses currently being offered at the University of Calgary. Under what conditions is each

*asked by Sue on March 22, 2013* -
## Discrete Math

Find f(1), f(2), and f(3) if f(n) is defined recursively by f(0) = 1 and for n = 0, 1, 2, . . . • f(n+1) = f(n) + 2 So, would it be f(n) = f(n+1) + 2? Or would I just keep it like the original and plug in 1, 2, 3. Thanks for any helpful replies.

*asked by Francesca on March 26, 2011* -
## Discrete Math

A quiz consists of 3 multiple choice questions, each of which have 10 answer choices. You are allowed three attempts at the quiz. What is the probability that someone would end up with a perfect score for the quiz simply by guessing the answers?

*asked by C on December 16, 2015* -
## Discrete Math

Congruence True or False: (give reason) _ __ 2 ∈ 18 (mod 8) Can someone please help with this problem? I'm confused. . . Thanks for any helpful replies.

*asked by Francesca on March 14, 2011* -
## Discrete Math

Using the ordinary alphabet and allowing repeated letters, find the number of words of length 8 that have at least one C. What's the difference between the wording of "exactly one" and "atleast one"?

*asked by Adedeji Ogunba on November 25, 2018* -
## discrete math

If a and b are positive integers, prove that: ab = gcd(a,b)*lcm(a,b). Can visualize this being true and easily create examples just don't know how to prove algebraically. well the gcd of any two number can be found by multiplying the two numbers together

*asked by Rom on March 8, 2007* -
## Discrete Math

I was hoping if you could help me to solve this problem. Thank you. A department wants to schedule final exams so that no student has more than one exam on any given day. There are 7 vertices of degrees 3,3,4,4,4,5,6 which show the courses that are being

*asked by yengiang on April 22, 2011* -
## Discrete Math

A professor gave his 40 students a test with three questions. Every student answered at least one question. Ten didn't answer the first question. 14 didn't answer the second question. 12 didn't answer the third question. If 18 students answered all three

*asked by Ajun on September 26, 2017* -
## discrete math

Find the solution to the following lhcc recurrence: an=3nan−1 for n2 with initial conditions a0=4.

*asked by cjones on April 20, 2012* -
## Discrete Math

Question : Consider the following sentences and prove that "Diana will win the game" 1.All Players are clever. 2.Anyone who is clever and dedicated can play the game well. 3.Anyone who is playing the game well will win his/her game. 4.Diana is a dedicated

*asked by Arya on October 9, 2019* -
## discrete math

Find the solution to the following lhcc recurrence: an=3nan-1 for n >or equal to with initial conditions a0=4

*asked by cjones on April 16, 2012* -
## Discrete Math

1.Using the principle of inclusion-exclusion find the numbers of integers between 1 and 1000 (inclusive)that are divisible by at least one of 2,3,5,or 7? 2.A drug store sells gum, candy, and playing cards. 15 teenagers are in the store...the clerk notes

*asked by Abbey on April 16, 2012* -
## discrete math

How many strings of five uppercase English letters are there (a) that start or end with the letters BO (in the order), if letters can be repeated? (inclusive or) (b) that start with an X, if letters can be repeated? (c) that start with the letters BO (in

*asked by carlton on April 3, 2012* -
## discrete math

Q:You have borrowed $8000 from the bank. Suppose you want to repay a fixed amount of money for each of the following n years (except possibly the last year), and the annual interest rate r does not change in these n years. For example, if r = 10% and you

*asked by akash on May 1, 2017* -
## Discrete Math

3. A club with 8 women and 6 men needs to choose two different members to be president and vice president (combination or permutation). a. In how many ways is this possible? b. In how many ways is this possible if women will be chosen as president and a

*asked by Peace on April 30, 2015* -
## Discrete Math

Solve the recurrence relation a_n = -6a_n - 1 + 7a_n-2, n ≥ 2, given a₀ = 32, a₁ = -17. This is what I have figured out so far: polynomial: x² + 6x - 7 distinct roots: 1 and -7 I do not understand how to find C₁ and C₂. How do I complete this

*asked by Francesca on April 5, 2011* -
## Discrete Math

Which of these relations on {0, 1, 2, 3} are equivalence relations? Justify the relation(s) that are not equivalent. R1: {(0,0), (1,1), (2,2), (3,3)} R2: {(0,0), (1,1), (1,3), (2,2), (2,3), (3,1), (3,2), (3,3)} R3: {(0,0), (0,1), (0,2), (1,0), (1,1),

*asked by Laurey on February 8, 2011* -
## Discrete math

Total ten pair of gloves are there. If I choose five gloves at random then whats the probability that there is at least one matched pair? What is the probability that I pick at least one right glove and one left glove?

*asked by Genie_math on October 3, 2012* -
## Discrete Math

How many handfuls of 15 are possible with at least one piece of each flavor - 50 cherry, 50 strawberry, 40 orange, 70 lemon, and 40 pineapple by assuming the pieces of flavor are identical?

*asked by Terri on October 27, 2011* -
## Discrete Math

Is this correct? • Using the Principle of Inclusion-Exclusion, find the number of integers between 1 and 2000 (inclusive) that are divisible by at least one of 2, 3, 5, 7. A = {n| 1 ≤ n ≤ 2000, 2 |n} B = {n| 1 ≤ n ≤ 2000, 3 |n} C = {n| 1 ≤ n

*asked by Francesca on April 12, 2011* -
## discrete math

Q6:What if the bookshelf is circular, that means you cannot choose the first and last books simultaneously? Count the number of ways to choose 6 books out of 20 books on a circular bookshelf such that no two adjacent books are selected.

*asked by akash on May 2, 2017* -
## DISCRETE MATH

We have a relation R on Z+ defined as follows: mRn if and only if m|n. Determine the set B = {n ∈ Z|52Rn}. Thanks

*asked by Anonymous on June 1, 2015* -
## DISCRETE MATH

How many different strings can be made from the letters in STATISTICS, using all the letters

*asked by brenda on September 29, 2014* -
## Discrete Math

How many ways can you get a bunch of 4 books to give a friend if you have 30 books (15 novels, 10 history book and 5 math books)?

*asked by Martin on November 1, 2011* -
## Discrete Math

Of the nine (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal and Ida), five of them stand in a row for a picture, how many ways can this be done if Ed and Gail are standing next to each other in the picture?

*asked by Jason on October 27, 2011* -
## Discrete Math

Use mathematical induction to prove the truth of each of the following assertions for all n ≥1. 5^2n – 2^5n is divisible by 7 If n = 1, then 5^2(1) - 2^5(1) = -7, which is divisible by 7. For the inductive case, assume k ≥ 1, and the result is true

*asked by Francesca on March 23, 2011* -
## Discrete Math

Consider the following relation on R1, the set of real numbers R1 = {(1,1), (1,2), (2,1), (2,2), (3,3), (4,4), (3,2), (2,3)} Determine whether or not each relation is flexible, symmetric, anti-symmetric, or transitive. * Reflexive because the relation

*asked by Laurey on February 8, 2011* -
## Discrete Math

An arithmetic sequence begins, 116, 109, 102 Find the 300th term of this sequence.

*asked by Francesca on March 28, 2011* -
## discrete math

in how many ways can 4 different prizes be given to any 4 of 10 people if no person receives more than 1 prize? help please and explain!!!!!!

*asked by kennedy on September 15, 2008* -
## discrete math

Nine people on a baseball team are trying to decide who will play which position. a. in how many different ways could they select a person to be pitcher? b. after someone has already been selected as pitcher, how mandy different ways could they select

*asked by kennedy on September 15, 2008* -
## discrete math

Find the solution to the following recurrence: an=3an−1+7 for n2 with initial conditions a0=7

*asked by cjones on April 20, 2012* -
## discrete math

Suppose that a department contains 10 men and 17 women. How many ways are there to form a committee with 6 members if it must have strictly more women than men?

*asked by carlton on April 8, 2012* -
## Discrete Math

1. Assume that n is a positive integer. Use the proof by contradiction method to prove: If 7n + 4 is an even integer then n is an even integer. 2. Prove: n is an even integer iff 7n + 4 is an even integer. (Note this is an if and only if (iff) statement.

*asked by Math help on February 21, 2008* -
## Discrete math

There are eighteen guard posts. How many ways can 25 not indistinguishable (That is, they are distinguishable.)guards be distributed to the guard posts, so that no post is empty? Try - (25 choose 18) ??

*asked by Genie_math on October 3, 2012* -
## Discrete Math

a) Show that the relation R on Z x Z defined by (a , b) R (c, d) if and only if a + d = b + c is an equivalence relation. b) Show that a subset of an anti symmetric relation is also anti symmetric. c) Suppose that R is a symmetric relation on a set A. Is R

*asked by Confused!! on March 15, 2012* -
## Discrete Math

You have two decks of 26 cards. Each card in each of the two decks has a different letter of the alphabet on it. You pick at random one card from each of the two decks. A vowel is worth 3 points and a consonant is worth 0 points. Let X = the sum of the

*asked by Martin on November 15, 2011* -
## discrete math

Q: Count the number of passwords with following constraints. Assuming digits = {0, 1, …..9}, letters = {a, b, ….. y, z} (a) 5 characters which are digits or letters. (b) 4 characters which are digits or letters, with at least 1 digit. (c) 4 characters

*asked by akash on May 1, 2017* -
## discrete math

"a club with 20 members must choose a three-person committee and a five-person committee. how many ways can the two committees be chosen if the committees can overlap? how many ways can the two committees be chosen if the committees cannot overlap?".

*asked by Caren on May 11, 2011* -
## discrete math

Fill in the blanks: For all sets A and B, if A is in the set of B, then A union B in in the set of B. Proof: Suppose A and B are any sets and A in in the set of B. [we must show that __________] Let x be and element of _______. [we must show that

*asked by heidi on April 15, 2011* -
## discrete math

Let A= {for all m that's an element of the integers | m=3k+7 for some k that's an element of positive integers}. Prove that A is countably infiite. Note: you must define a function from Z+ to A, and then prove that the function you definied is a bijection

*asked by Samantha on December 4, 2010* -
## Discrete Math

7.A group has 9 women and 7 men. d. Suppose 2 members of the group refuse to work together. How many subgroups of 5 can be chosen 8. In how many ways can 16 people be seated: a. In a row, if 4 of the 16 do not want to sit next to one another b. In a row,

*asked by Justin on November 4, 2010* -
## Discrete Math

A multiple choice test consists of eight questions, each of which has five choices. Each question has exactly one correct answer. William guesses randomly at each answer. What is the probability that he gets six or fewer questions correct?

*asked by Shalini on August 14, 2015* -
## Discrete Math

Directions: Find the quotient and the remainder when the first polynomial is divided by the second. #9. 3x^4 – 2x^3 + 5x^2 + x + 1;x^2 + 2x

*asked by Sarah on September 15, 2011* -
## Discrete Math

Pattern Matching 6. Build the Boyer-Moore last table for the following pattern/alphabet pairs. (a) “giggling”’ {g, I, l, n} (b) “mimimi” , {i, m} (b) ANSWER: i m 6 5 14. Search for the pattern “pie” in the text “pickled peppers”. Create a

*asked by JayLQue on April 20, 2011* -
## Discrete Math

Let A={0,1,2,3,4}. Define a function f from A to A by f(n)=2n mod 5. a/ Is f one-to-one? b/ Is f onto? Could you show me how to solve this problem, please? I have no idea what this function is. Your help is greatly appreciated.

*asked by yengiang on April 16, 2011* -
## Discrete Math

Let a, b, c, and d be integers, and let n be a positive integer. Prove that if a is congruent to c mod n and b is congruent to d mod n, then (a-b) is congruent to (c-d) mod n

*asked by Samantha on December 4, 2010* -
## discrete math

If a and b are positive integers, and m=lcm(a,b), explain why m divides any common multiple of a and b. The answer is in the definition of lcm:] the smallest multiple that is exactly divisible by every member of a set of numbers. So if m is divisble by a

*asked by romulo on March 7, 2007* -
## discrete math

use a direct proof to show that the product of two odd numbers is odd. Proofs: (all the nos. i used are odd) 3 x 3 = 9 5 x 9 = 45 7 x 3 = 21 Yes, but you didn't prove the statement for "all" odd integers, only the odd integers you selected. uhm..he didn't

*asked by audryana on September 27, 2006* -
## discrete math

Suppose that a department contains 10 men and 17 women. How many ways are there to form a committee with 6 members if it must have strictly more women than men?

*asked by carlton on April 3, 2012* -
## Discrete Math

7.A group has 9 women and 7 men. d. Suppose 2 members of the group refuse to work together. How many subgroups of 5 can be chosen 8. In how many ways can 16 people be seated: a. In a row, if 4 of the 16 do not want to sit next to one another b. In a row,

*asked by Justin on November 4, 2010* -
## discrete math

which positive integers less than 12 are relatively prime to 13 Since 13 has no factors, then all integers 2, 3, 4, 5, 6....11 are relatively prime to 13

*asked by thisha on November 6, 2006* -
## discrete math

Q 8: Count the number of 01-strings with following constraints. (a) The length is 8. Number of 1s is 2 more than number of 0s. (b) The length is 8. Number of 1s is 3 more than number of 0s. (c) The length is 9. Number of 1s is 3 more than number of 0s.

*asked by akash on May 1, 2017* -
## Discrete Math

Prove that (A ∩ B) ∪ C= A ∩ (B ∪ C) if and only if C ⊆ A. I really need some help on structuring the proof!

*asked by Mimi on February 25, 2016* -
## Discrete Math

There are 150 students taking Discrete Mathematics II, Calculus II, and Physics I courses. Of these 51 are taking Discrete Mathematics II, 111 are taking Calculus II, and 63 are taking Physics I. There are 41 taking Discrete Mathematics II and Calculus II,

*asked by Anonymous on April 6, 2014* -
## Discrete Math

Let n be positive integer greater than 1. We call n prime if the only positive integers that (exactly) divide n are 1 and n itself. For example, the first seven primes are 2, 3, 5, 7, 11, 13 and 17. (We should learn more about primes in Chapter 4.) Use the

*asked by Ron on April 5, 2013* -
## Discrete math

I need to find the coefficient of x^18 y^32 in (x+y)^50. I understand that we have to use the binomial theorem. I know how to find the coefficient for example x^18 but here we have "x" as well as "y" which I have no idea about.

*asked by Genie_math on October 3, 2012* -
## Discrete Math

Statements P->Q, ~R->(S->T), R v(P v T), and ~R are true. What is the truth value for the statement, (Q v S)?

*asked by Jerry on August 1, 2012* -
## Discrete Math

Hi there I'm confused as to how to start this problem, any help at all would be great thanks! John Sununus was once the governor of New Hampshire, and his name reminds one of the authors of a palindrome (a words which is spelt the same way forwards as

*asked by James on April 12, 2011* -
## Discrete Math

I have a review problem I am having problems with. This is the problem: Be able to show the function, g(x) is O(f(x)) numerically as we have done in class Use the definition of O-notation to prove that 2x^2+3x+4 is O(x^2) (Do not use the theorem on

*asked by Elisabeth on April 14, 2010* -
## discrete math

Q 7: What is the number of `Hello's printed by the pseudo code below? (for i from lo to hi exhaust i between lo and hi inclusive, and is a empty loop when lo is greater than hi) (a) for i from 1 to n for j from 1 to i - 1 for k from 1 to j - 1 print

*asked by akash on May 1, 2017* -
## discrete math

Q: There are n identical balls and m different bins. Let Bn,m be the total number of way to put n balls in m bins. (a) What are B1,1, B2,1, B1,2, B2,2, B3,2? (b) Express Bn,m in terms of Bk;m-1, for k = 0,….. n.

*asked by akash on May 1, 2017* -
## discrete math

A bubble sort begins with the array: 372418 Work through the lists obtained at each step of the bubble sort. Complete the table below for the intermediate step where 7 is at position four in the array. [][][]7[][]

*asked by AJ on March 9, 2017* -
## Discrete Math

Let A = {x ∈ R| cos x ∈ Z}, B = {x ∈ R| sin x ∈ Z}. Is A ⊆ B? Is B ⊆ A? Is either A or B a proper subset of the where other?

*asked by Alex on February 22, 2016* -
## Discrete Math

12 A computer science department has a probability of 0.35 that a senior receives a job offer in IT before graduation. Random select 8 senior students • What is the probability that 5 students received offers before graduation? • What is the

*asked by Peace on April 30, 2015* -
## Discrete Math

Please help with this problem. Thanks a/ Show that for any real number x, if x>1 then |x^4|=< |23x^4 + 8x^2 + 4x| b/ Show that for any real number x, if x>1 then |23x^4 + 8x^2 + 4x| => |x^4| c/ Use the big Theta and big O-notations to express the results

*asked by yengiang on April 29, 2011* -
## Discrete Math

So = 2 S1 = 5 Sn = - Sn - 1 + nSn - 2, n >_ 2 How do I interpret the value of n? Is this number equivalent to S1, S0, or 2? I have tried each option; finding S3 is difficult because I don't know what value to multiply Sn-2 with, when solving for S2. Your

*asked by Compstudent on April 1, 2011* -
## Discrete Math

Use mathematical induction to establish the following formula. n Σ i² / [(2i-1)(2i+1)] = n(n+1) / 2(2n+1) i=1 Thanks for any helpful replies :)

*asked by Francesca on March 22, 2011* -
## Discrete Math

Use mathematical induction to prove the truth of each of the following assertions for all n ≥1. n³ + 5n is divisible by 6 I really do not understand this to much. This is what I have so far: n = 1, 1³ - 5(1) = 6, which is divisible by 6 Then I really

*asked by Francesca on March 21, 2011* -
## Discrete Math

Prove DeMorgan's Laws for sets? Let A, B, and C be sets. Then A - (B union C) = (A - B) intersection (A - C) and A - (B intersection C) = (A - B) union (A - C) Counting problems using lists? 1.) A U.S. Social Security number is a nine-digit number. The

*asked by Chris on September 15, 2009* -
## Discrete Math

You are stranded on a deserted island, and along the way you stumble across a genie. He says he will get you off the island provided that you can meet his conditions. He hands you a 20-sided die, and says that you need to roll it 1000000 (one million)

*asked by Bob on April 29, 2007* -
## discrete math

Q6:What if the bookshelf is circular, that means you cannot choose the first and last books simultaneously? Count the number of ways to choose 6 books out of 20 books on a circular bookshelf such that no two adjacent books are selected.

*asked by akash on May 2, 2017* -
## discrete math

1.Let functions f and g be defined by f(x)=2x+1, and g(x)=x^2-2, respectively. Find a)(gof)(a+2) b)(fog)(a+2) 2.Let A={x:x≠2) and define f: A→R by f(x)=4x/(2x-1) . Is f is one- to- one? Find the range of f . Then find f^(-1) and hence determine the

*asked by rose on July 9, 2016* -
## Discrete math

TRUE OR FALSE ? Justify your answer. a. There exist real numbers a and b such (a+b)^2 = a^2 + b^2. b. For any real number x, there exists a unique number -x such that x + (-x) = 0. c. Any integer n is either odd or even. d. Any real number x can be written

*asked by Alfonso on March 3, 2016*

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