m men and n women are to be seated in a row so that no two women sit together. If `(m>n)` then show that the number of ways in which they can be seated as `(m!(m+1)!)/((m-n+1)!)` .

Explanation

There are total n women

there are n+1 places for women

`.^nP_r=(n!)/((n-r)!)`

`.^nP_n*.^(n+1)P_n=(n!)/((m-n)!)*((n+1)!)/((m+1-n)!)`

Total possible ways`=((m!)*(m+1)!)/((m-n+1)!)`