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

could you kindly explain me how this result is obtained

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- Oct 2nd 2011, 10:31 AManigeoexplanation of the given result of permutations
the number of permutations of n different things raken r at a time where k particular things

is given by (n-kpr-k) *(n-k+1).__always occur together in an assigned order__

could you kindly explain me how this result is obtained

- Oct 2nd 2011, 02:59 PMPlatoRe: explanation of the given result of permutations
I am not really clear on the setup.

Suppose we have $\displaystyle abcdefghijklm$, 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*$\displaystyle def$ in that order.

So we are going to permute $\displaystyle 8-3=5$ of these $\displaystyle 13-3=10$ letters $\displaystyle abcghijklm$.

Those 5 letter and the*block*make 6 things to permute.

$\displaystyle _{10}\mathcal{C}_5(6!)=_{10}\mathcal{P}_5(6)$.

You can make the generalizations.