Question

If 'm' men and 'n' women are to be seated in a row so that no two women sit together and m > n, then the number of ways in which they can be seated is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Given, no two women sit together i.e. every woman sits between two men.

The number of spaces available between m men = m+1

The number of ways in which n women can be arranged in m+1 places is${}^{m+1}{\text{P}}_n$

The number of ways in which they can be seated = $m!{\times }^{m+1}{\text{P}}_n$