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Math Help - probability help please

  1. #1
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    Smile probability help please

    How many 13 digit numbers are palindromes and have at least one place where a digit is doubled. A palindrome is the same read forwards or backwards, like bob, racecar, or 57975.

    For example:
    1234456544321
    9107772777019
    2497644467942


    1234567654321 Does not count, since it has no doubled digits.

    Answer: 4217031
    I need help with how to solve....Thanks and sorry if this is not advanced probability
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  2. #2
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    Quote Originally Posted by tony351 View Post
    How many 13 digit numbers are palindromes and have at least one place where a digit is doubled. Answer: 4217031
    I assume that a 13 digit number cannot begin with a zero.
    The create a 13 digit palindrome all we need is to create a seven digit number and reverse the order of the first six digits.
    Thus there are 9\left( {10^6 } \right) such palindromes.
    To count the number of those with no repeated digits, each time we select a digit we must select a different one the next time. That can be done in 9\left( {9^6 } \right) possible ways.
    So the answer: 9\left( {10^6 } \right) - 9\left( {9^6 } \right).
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  3. #3
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    stupid question

    Thank you so much for the solution, can you tell me where the 9 comes from? I know that's a crazy question but I have no clue. Thanks again in advance
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  4. #4
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    Quote Originally Posted by tony351 View Post
    Can you tell me where the 9 comes from?
    Simple. The number cannot began with a zero.
    Thus that are but nine choices for the first digit in the number.
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  5. #5
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    thank you

    See told you dumb question LOL. Thank you it makes since now
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