Question

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

Answer 1

Given r places, we first fill up 3 places by 3 particular things. This can be done in ^rP₃ ways.

Now, we have to fill remaining r − 3 places with remaining n − 3 things.

This can be done in ^{n − 3}P_{r − 3} ways.

Thus, the required number of permutations will be ^rP₃ × ^{n − 3}P_{r − 3} ways.