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Math Help - explanation of the given result of permutations

  1. #1
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    explanation of the given result of permutations

    the number of permutations of n different things raken r at a time where k particular things always occur together in an assigned order is given by (n-kpr-k) *(n-k+1).


    could you kindly explain me how this result is obtained

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  2. #2
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    Re: explanation of the given result of permutations

    Quote Originally Posted by anigeo View Post
    the number of permutations of n different things raken r at a time where k particular things always occur together in an assigned order is given by (n-kpr-k) *(n-k+1).


    could you kindly explain me how this result is obtained

    I am not really clear on the setup.
    Suppose we have abcdefghijklm, the first thirteen letters of the alphabet. It seems that you are asking for the number of permutations of eight of those letters BUT among those eight must be the block def in that order.

    So we are going to permute 8-3=5 of these 13-3=10 letters abcghijklm.
    Those 5 letter and the block make 6 things to permute.
    _{10}\mathcal{C}_5(6!)=_{10}\mathcal{P}_5(6).

    You can make the generalizations.
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