1.

`m`men and `n`women ae to be seated in a row so that no twowomen 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» Correct Answer - `((m+1)!m!)/((m-n+1)!)`
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)!)`


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