$m$ men and $n$ women are to seated in a row so that no two women sit together. If $mn$ then show t

Question

$m$ men and $n$ women are to 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 is $\frac{\lfloor m \mid m+1}{\lfloor m-n+1}$.

Professor PC Thomas Classes · Answer

$m$ men can be seated in a row in $\underline{m}$ ways. Now there are $m+1$ places in which $n$ women can be arranged in ${ }^{(m+1)} P_{n}$ ways.\ $	herefore$ Total number of ways of $m$ men and $n$ women be seated\ $=\left\lfloor m .{ }^{(m+1)} P_{n}=\frac{\lfloor m \mid m+1}{\lfloor m-n+1}ight.$.