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Probability please help!

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The digits 2, 3, 4, 7, and 8 are each used once in a random order to form a five-digit number. What is the probability that the resulting number is divisible by 4? Express your answer as a common fraction.

  • Probability please help! -

    It means that numbers 2,3,7 have to be first so combination choose 3 out of 5 and then either 4 or 8 can be in the end which can be done in 2! ways. So 20ways out of possible 5!=120 so 20/120= 2/12=1/6

  • Probability please help! -

    if any number is divisible by 4 , then its last 2 digits must be divisible by 4
    e.g 43728 is divisible by 4 because 28 is divisible by 4
    whereas 72438 is not , even though its last digit is divisible by 4
    obviously it must be also be even,

    so the last two digits could be
    xxx28
    xxx48
    xxx24
    xxx84

    the number of cases for each of these
    = 3x2x1
    = 6

    e.g. for xxx28
    34728 , 37428 , 43728 , 47328 , 73428 , 74328

    so the number of cases which are divisible by 4 are 3(6) = 24
    but the total number of arrangements with no restrictions are 5! = 120

    prob of divisible by 4 = 24/120 = 1/5

  • Probability please help! -

    thanks

  • Probability please help! -

    none of these answers are correct lol

  • Probability please help! -

    You are all wrong!!!! Its 3/10

  • Probability please help! -

    hahaha is RIGHT!!!!!!! ur all worng!!
    :) :(

  • Probability please help! -

    For last 2 digits, you forgot xxx32 and xxx72. There are 4 * 5 = 20 ways to choose the last two digits, and they are all equally likely, so the probability that the number is divisible by 4 is (# of ways to choose last 2 digits such that the number is divisible by 4)/ways to choose last 2 digits = 6/20 = 3/10.

  • Probability please help! -

    A number is divisible by 4 if and only if the number formed by its last two digits is divisible by 4. Using the given digits, we find that the only two-digit numbers that are divisible by 4 are 24, 28, 32, 48, 72, and 84.

    There are $5 \cdot 4 = 20$ ways to choose the last two digits, and they are all equally likely, so the probability that the number is divisible by 4 is $6/20 = \boxed{3/10}$.

  • Probability please help! -

    A number is divisible by 4 if and only if the number formed by its last two digits is divisible by 4. Using the given digits, we find that the only two-digit numbers that are divisible by 4 are 24, 28, 32, 48, 72, and 84.

    There are $5 \cdot 4 = 20$ ways to choose the last two digits, and they are all equally likely, so the probability that the number is divisible by 4 is $6/20 = \boxed{3/10}$.

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