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Math Help - Permutations & Combinations

  1. #1
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    Permutations & Combinations

    Q: Find out how many 3 figure numbers, lying between 100 and 999 inclusive, have 2 and only 2 consecutive figures identical.

    Thank you for helping! ^^
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  2. #2
    Senior Member vincisonfire's Avatar
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    You can choose  \frac{10!}{2! \cdot (10-2)!} sets of two numbers and you can permute them 2 times.
    If you pick eg 2 and 9, you can make 992 and 229.
    You need to consider that 0 and 1 can only make 100 so do -10 at the end.
    I think you should get 80 numbers in the end.
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  3. #3
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    ^ But the answer I was given is 162 numbers....
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  4. #4
    Senior Member vincisonfire's Avatar
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    I just realize I'm wrong. Sorry!
    Let's do it like this.
    You have 9 possibilities for first number and 9 for the second when the second is repeated. 9 x 9 = 81
    You have 9 possibilities for first number and 9 for the second when the first is repeated. 9 x 9 = 81
    Way more simple and works well. Less esthetic although.
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