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Math Help - how many combinations if space is truncated

  1. #1
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    how many combinations if space is truncated

    I know there are 7! combinations of the numbers 1 to 7.

    But how many combinations of the numbers 1 to 7 are there if only five numbers are allowed. For example, if there are 7 people and only 5 chairs how many different combinations of seated people are there?


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  2. #2
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    Re: how many combinations if space is truncated

    Quote Originally Posted by rainer View Post
    I know there are 7! combinations of the numbers 1 to 7.
    But how many combinations of the numbers 1 to 7 are there if only five numbers are allowed. For example, if there are 7 people and only 5 chairs how many different combinations of seated people are there?
    You are using the wrong word, combinations.
    You seem to be talking about permutations.
    A permutation has order but combinations have nothing to do with order.
    The number of permutations of N objects taken k, _N\mathcal{P}_k=\frac{N!}{(N-k)!}

    So _7\mathcal{P}_7=\frac{7!}{(0)!}=7!

    and _7\mathcal{P}_5=\frac{7!}{(2)!}=7\cdot 6\cdot 5\cdot 4\cdot 3
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