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Math Help - Permutations

  1. #1
    Junior Member
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    Permutations

    What is the total number of ways in which six 't' signs and four 't' signs can be arranged in a line such that no two '-' signs occur together?

    I have come up with possble orderings of:

    t - t - t - t t - t - : having 2 t's together

    t t t - t - t - t - : having 3 t's together

    The answer is 35.

    I come up with 3!4! + 4!4! from the above method so I must be doing something very wrong
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  2. #2
    MHF Contributor
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    There are 7 places between t's and at both ends. Each place can accommodate at most one -. Therefore, the answer is {7\choose 4}.
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