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Thread: Chance of guessing 4 numbers from 7 - should be easy!?

  1. #1
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    Chance of guessing 4 numbers from 7 - should be easy!?

    I have what appears (to my non-mathematical brain) to be a relatively simple probability problem, but I don't know how to go about solving it. Perhaps someone here could help, and "explain their working" so that I can figure it out for myself in future.

    Here's the problem:

    • I choose 4 numbers from 1-49
    • A random number generator selects 7 numbers from 1-49, with each number only appearing once
    • What is the probability that my 4 chosen numbers all appear within the selection of 7?
    • The sequence in which the numbers appear is not important.


    Thanks for your help!
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  2. #2
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    Re: Chance of guessing 4 numbers from 7 - should be easy!?

    4 numbers need to be "matched"; so:
    4/49 * 3/48 * 2/47 * 1/46 = 1/211876 ;
    same as 49C4.
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  3. #3
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    Re: Chance of guessing 4 numbers from 7 - should be easy!?

    Quote Originally Posted by visualthinker View Post
    • I choose 4 numbers from 1-49
    • A random number generator selects 7 numbers from 1-49, with each number only appearing once
    • What is the probability that my 4 chosen numbers all appear within the selection of 7?
    • The sequence in which the numbers appear is not important.
    There are $_{49}\mathscr{C}_7=\dbinom{49}{7}=85,900,584$ ways for the random number generator to select 7 numbers from 1-49. Of those there are $_{45}\mathscr{C}_3=\dbinom{45}{3}=14,190$ which contain any four given (selected) numbers.
    Thanks from SlipEternal and Vinod
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