Question

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

Answer 1

Since, m men and n women are to be seated in a row so that no two women sit together. This could be shown as
`xx M_(1) xx M_(2) xx M_(3) xx .. Xx M_(m) xx`
which shows there are (m + 1) places for n women.
`therefore` Numebr of ways in which they can be arranged
`= (m)! " "^(m + 1)P_(n)`
`= ((m)! * (m + 1)!)/((m + 1 - n)!)`