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Math Help - probability of repeating digit

  1. #1
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    probability of repeating digit

    Hi!

    What is the probabilty that in a 10-digit number, digit 7 repeats 6 times (no more or less, exactly)?

    or in other words, what is the probability that in a random 10-digit number there will be 6 sevens.

    thanks
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  2. #2
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    Re: probability of repeating digit

    Quote Originally Posted by Kiiefers View Post
    What is the probabilty that in a 10-digit number, digit 7 repeats 6 times (no more or less, exactly)?
    or in other words, what is the probability that in a random 10-digit number there will be 6 sevens.
    First by "10-digit number' you must mean the leading digit cannot be 0.
    So there are 9\cdot 10^9 10-digit numbers.

    Of those, there are \binom{9}{5}\cdot 9^4 that begin with a seven and have exactly five other sevens.

    There are 8\cdot\binom{9}{6}\cdot 9^3 that do not begin with a seven and have exactly six sevens.
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  3. #3
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    Re: probability of repeating digit

    Thanks.
    What those brackets in this case mean?

    Combinations or variations?
    Last edited by Kiiefers; March 13th 2013 at 03:37 AM.
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  4. #4
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    Re: probability of repeating digit

    Quote Originally Posted by Kiiefers View Post
    What those brackets in this case mean?
    Combinations or variations?

    \binom{N}{k}=\frac{N!}{k!(N-k)!}
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