Question

The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
(a) 4! × 3!
(b) 4!
(c) 3! × 3!
(d) none of these.

Answer 1

(a) 4! × 3!
According to the question, 3 men have to be 'consecutive' means that they have to be considered as a single man.
But, these 3 men can be arranged among themselves in 3! ways.
And, the remaining 3 men, along with this group, can be arranged among themselves in 4! ways.
∴ Total number of arrangements = 4! × 3!