The number of ways of arranging 18 boys such that 3 particular boys are always separate is equal to

Step-by-step solution

First arrange 15 boys in 15 ! ways. 16 gaps will be created. Select any 3 gaps out of 16 gaps in C 16 3 ways. Arrange 3 boys to be separated in these selected 3 gaps in 3 ! ways. Number of ways = 15 ! × C 16 3 × 3 ! = 15 ! × P 16 3