Mark the correct alternative in the following:

The number of permutations of n different things taking r at a time when 3 particular things are to be included is

Primarily, excluding the 3 things which are to be included, we have to select (r - 3) things from (n - 3), this can be done in ^{n – 3}C_{r – 3} ways.

Now, the 3 particular things can be selected from 3 remaining things only in 1 way.

And the selected r things can be arranged in r! ways.

So, the number of permutations of n different things taking r at a time when 3 particular things are to be included is = r! ^{n – 3}C_{r – 3}