posted by .

A)If a license plate consists of 2 letters followed by 3 digits or 3 letters followed by 2 digits, how many license plates can be created?

B)You are given an exam with only 9 questions. if each question has 4 choices, howmany different possible answers can you have for the entire exam?

C)If you have 20 students in your class, how many different ways can a committee of 5 be chosen if 1 person on the committee will be the president?

E) 25 people run a marathon. The first 6 people to finish will receive an award for their finish position. How many ways can the awards be given?

F) How many distinct arrangements of the letters in the word UNUSUAL can be made?

G) How many 4- letter words can be fromed by slection four letters from the word UNIFORM?

i know that you use ncr and ncp, but i don't understand can someone please show work! thanks for your time yoo

I assume the letter and numbers can be repeated, for example AA111
In that case all slots are independent, you do not have to do combinations
If there are 26 letters (in practice you do not want to use them all because 0 and O look to much alike etc)
ways to get 2 letters = 26*26
ways to get 3 digits = 10*10*10 (using 0--9)
so 26*26*1000
you can do the second half

• Math -

B is done the same as A, 4^9 (huge)

C Ignoring the president bit, how many combinations of 20 students taken 5 at a time?
C(n,r) = n!/[(r!(n-r)! ]
= 20! / [5! (15!) ]
= 20*19*18*17 *16 /[5*4*3*2]
= 19 * 3* 17 * 16
now you have in each of these 4 groups of five students, five choices for president
so multiply that answer by 5*5*5*5

That is enough, you should be able to continue

E) 25 people run a marathon. The first 6 people to finish will receive an award for their finish position. How many ways can the awards be given?
----------------------------------
Well E is different from D in that the order of the 6 people matters (one gets blue ribbon, one red ribbon etc) so it is not just a combination of 6 out of 25
but is called the "permutations" of 25 taken 6 at a time:
P(n,r) = n!/(n-r)!
=25!/19! = 25*24 *....20

U N U S U A L
This would be permutations of 7 objects except that we have three identical Us.
so permutations of 7 objects = 7!
but we have embedded in there the permutations of three objects
3!
so I get
7!/3! = 7*6*5*4

## Similar Questions

1. ### Math

A license plate is to consist of two letters followed by three digits. How many different license plates are possible if the first letter must be a vowel, and repetition of letters is not permitted, but repetition of digits is permitted?
2. ### algebra

In Utah, a license plate consists of 3 digits followed by 3 letters. The letters I, O, and Q are not used, and each digit or letter may be used more than once. How many different license plates are possible?
3. ### math check my work

a license plate has 2 letters followed by 4 digits.how many license plates are possible if the digits and letters can be repeated?
4. ### math please check my work

a license plate has 2 letters followed by 4 digits.how many license plates are possible if the digits and letters can be repeated?
5. ### Math

A state creates license plates that each contain two letters followed by three digits. The first letter must be a vowel ( A, E, I, O, U ) and duplicate letters and digits are allowed. How many different license plates are possible?
6. ### survey of math

A license plate is to consist of 2 letters followed by 3 digits. Determine the number of different license plates possible if repetition of letters and numbers is not permitted?
7. ### statistics

A license plate is to have 3 digits followed by 2 uppercase letters. What is the number of different license plates possible if repetition of numbers and letters is not permitted?
8. ### Computers

In Python - A state creates license plates, each containing two letters followed by three digits. The first letter must be a vowel (A,E,I,O,U), and duplicate letters and digits are allowed. The second letter can be any letter of the …
9. ### College probability and statistics

The current license plates in New York State consist of three letters followed by four digits. ( i ) How many possible distinct license plates can there be?
10. ### math

License plates consist of letters and/ or digits. Calculate the number of licence plates that could be formed in each province or territory. Assume all numbers and letters are possible. a) Ontario, with 4 letters followed by 3 digits …

More Similar Questions