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Math Help - Counting problem

  1. #1
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    Counting problem

    If Set S = {1,2,3,4}, how many permutations of \mathcal{P}{(S)} are there so that no subset is ever followed by a subset of smaller size?

    So this is what I did:

    Possible sizes are 0, 1, 2, 3, 4
    { 4 \choose 0 },{ 4 \choose 1 },{ 4 \choose 2 },{ 4 \choose 3 },{ 4 \choose 4 }

    which is 1, 4, 6, 4, 1, respectively

    So I choose smallest first, which is still in respective order, so:

    I did 1! * 4! * 6! * 4! * 1! which came out to be 414720

    However, I doubt this is right. Anyone know if I did anything wrong?

    Thanks.
    Last edited by Plato; March 16th 2010 at 05:21 PM.
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  2. #2
    Senior Member Dinkydoe's Avatar
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    I assume you mean permutations of \mathcal{P}(S) (the set of all subsets of S)

    What you did was indeed correct. Not very surprising, considering the total amount of permutations of \mathcal{P}(S) is 16!
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  3. #3
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    Yeah whoops that's what I meant. I wasn't sure if this was correct because it seemed too easy for an assignment question. Anyways, thanks for the help!
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