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Math Help - **urgent: Desperate Probability Question**

  1. #1
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    Unhappy **urgent: Desperate Probability Question**

    I need to find a generalized equation for this problem:

    Given the digits 1, 3, 6 and 9, find the probability that a 4-digit number is formed by using each of them only once and is divisible 7.

    I found that there are 24 numbers and 4 are divisible by 7 for those specific digits but when I go to generalize this (and attempt to write an equation) I am lost. I did this via a tree diagram but cannot solve to get a general equation, ie, if 4 random digits are picked, and arranged to make a 4 digit number, what is the probabilty that they are divisible by 7 (there has to be an equation where you can plug in 4 numbers and do get the probability)?

    I am lost and need help desperately as this is due in a few days. A push in the right direction PLZ!! thnx!!
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  2. #2
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    Assuming they're the only digits that can make up a number...

    The probability of them being used once is 4!/4^4 = 3/32

    So if 4 are divisible by 7, then it's 4/4^4 = 1/64
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  3. #3
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    Is it just the first part of the question that says you use those numbers? Can the general part use all the digits 0 to 9?

    If so, then 9999/7 = 1428.4

    So there are 1428 numbers from 0 to 9999 divisible by 7

    1428/10000 = 357/2500
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