`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

`((m+1)!m!)/((m-n+1)!)`

Explanation

m men can be seated in m! ways, creating (m+1) places for n ladies to sit.
n ladies in (m+1) places can be arrnanged in `.^(m+1)P_(n)` ways.
`therefore` Total ways `=m!xx .^(m+1)P_(n)`
`m!xx((m+1)!)/((m+1-n)!)=((m+1)!m!)/((m-n+1)!)`