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Math Help - Different Combinations

  1. #1
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    Different Combinations

    I have a question:
    You have 10 slots in which to put the numbers 1-5 and each number must be used twice but no more than twice. (ex: 5 5 4 4 3 3 2 2 1 1 ex. 5 4 5 3 2 4 1 2 1 3.) How many different combinations are there? ( I think i know the answer but i just want to double check)
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  2. #2
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    Have you tried [10!]/[2^5]?
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  3. #3
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    No i didnt, is that the answer?
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  4. #4
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    Hello, Chilly!

    Plato is absolutely correct . . .


    You have 10 slots in which to put the numbers 1 to 5'
    and each number must be used twice but no more than twice.
    How many different permutations are there?
    Suppose we had ten different numbers.
    . . There would be 10! arrangements.

    But since there two 1's, they can be switched without creating a new arrangement.
    . . Hence, they make our answer too large by a factor of 2.

    And since there two 2's, they too can be switched.
    . . Hence, they make our answer too large by a factor of 2.

    Similarly, two 3's, two 4's and two 5's can be switched.
    . . Each makes the answer too large by a factor of 2.

    Hence, our answer is too large by a factor of 2^
    5.

    . . - . . - . . - . . 10!
    The answer is: .-----
    . . . - . . . . . . . 2^
    5

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  5. #5
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    Sweet, thanks guys!
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