explanation of the given result of permutations

• Oct 2nd 2011, 10:31 AM
anigeo
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

• Oct 2nd 2011, 02:59 PM
Plato
Re: explanation of the given result of permutations
Quote:

Originally Posted by anigeo
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 $\displaystyle abcdefghijklm$, 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.