1.

mmen andnwomen are to be seated in a row so that no twowomen 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)!)`.

Answer» 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)!)`


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