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Math Help - 6 digit number

  1. #1
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    6 digit number

    we want to create a 6 digits number from the digits 1-5, and to keep the condition that each of the 5 digits, appear at least once. what is the probability that the number 11 ( the digit 1 twice ), will appear ? ( meaning what is the prob that 1 will appear twice and in a row )

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  2. #2
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    Quote Originally Posted by WeeG View Post
    we want to create a 6 digits number from the digits 1-5, and to keep the condition that each of the 5 digits, appear at least once. what is the probability that the number 11 ( the digit 1 twice in a row )?
    In each of those 6-digit numbers there will be five different digits and one which repeats.
    There are 5 ways to pick the one that repeats.
    Then there are \frac{6!}{2} ways to arrange these six digits.

    There are 5! ways arrange the string “112345” so that the 1’s are together.
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