math

The digits 2, 4, 6, 8 and 0 are used to make five-digit numbers with no digits repeated. What is the probability that a number chosen at random from these numbers has the property that the digits in the thousands place and ten's place are each larger than their neighboring digits.
a)5/48
b)11/96
c)1/8
d)13/96
e)7/48
So I know that it's out of 4 * 4! combinations because you can't have the zero as the first digit, how do I find how many numbers meet the condition?

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. Case1: the 6 in in thousand place and 8 in the tens place, leaving the 0,2,4
    _6_8_ -----> 2x2x1 = 4
    Case2:
    _8_6_ -----> 2x2x1 = 4
    Case3:
    _8_4_ , the 6 must be the lead digit
    68_4_ ------> 2x1 = 2

    a total of 10
    prob(your event) = 10/96 = 5/48

    it would be simple to actually list the numbers

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    Solve the mathematical puzzle. Determine the digits of Q from these clues. The first and third digits of Q are even. The second and fourth digits of Q are odd. The first digit is two times the fourth digit. The first and second

  2. maths

    can you replace the stars with figures **** x 3 ______ ***** the whole calculation uses each of the digits 0-9 once and once only the 4 figure number contains three consecutive numbers which are not in order. the third digit is

  3. math

    Neelesh is fond of playing number games. Once when his friends were present he challenged them. He said that he has thought of a five-digit number and anyone who guesses it correctly can use his cycle for a full day. ‘To help

  4. College

    Three(3) digit numbers can be formed from the digits 0,1,3,5,7 and 8. How many numbers can be formed without repeats. (A) if the 3 digits numbers must be divisible by 5. (b) if the 3 digits number must be a multiple of 2

  1. math

    find how many six-digit numbers can be formed from the digits 2,3,4,5,6,7 (with repetitions) if a) numbers formed must be even b) the numbers formed must be divisble by 25 c) the odd digits must occupy even position (2nd, 4th,

  2. math

    While adding ten two-digit numbers the digits of one of the numbers were interchanged. As a result the sum of all the ten numbers increased by a value which was four less than that number. Three times the sum of the digits of the

  3. Maths

    In A Two Digit Number, The Sum Of The Digits Is 14. Twice The Tens Digit Exceeds The Units Digit By One.Find the Numbers.

  4. math problem

    My ID number is quite remarkable.Its a 9 digit number with the digits 1-9 appearing only once. The entire 9 digit nuymber is divisible by 9. If you remove the last digit, the remaining 8 digit number is divisible by 8. If you

  1. Math

    John chooses a 5-digit positive integer and deletes one of its digits to make a 4-digit number. The sum of this 4-digit number and the original 5-digit number is 52713. What is the sum of the digits of the original 5-digit number?

  2. Mathe

    The number has two digits. Both of the digits are even.the digit in the tens place is greater that the digit in the unit (or ones) place.the units (or ones digit) is not in the three times table. The tens digit is not double the

  3. math

    Find a six-digit even number containing no zeros and no repeating digits in which the first digit is four more than the second digit, the third digit is one less than the sixth digit, and the fourth and fifth digits when read as a

  4. Math

    A number has three distinct digits. The sum of the digits equals the product of the digits. How many three-digit numbers satisfy this condition?

View more similar questions or ask a new question.