$m$ men and $n$ women are to be seated in a row so that no two women sit together. If $m n$, then the number of ways in which they can be seated, is

Question

$m$ men and $n$ women are to be seated in a row so that no two women sit together. If $m > n$, then the number of ways in which they can be seated, is

Dr. Abubacker · Accepted Answer

(a)
First arrange $m$ men in a row in $m!$ ways. Since, $n < m$ and no two women can sit together in any one of the $m!$ arrangement, there are $(m + 1)$ places in which $n$ women can be arranged in $\ ^{m + 1}P_{n}$ ways.
$	herefore$ The required number of arrangements of $m$ men and $n$ women $(n < m)$
$= {m!}^{m + 1}P_{n} = \frac{m!(m + 1)!}{(m - n + 1)!}$

Q. $m$ men and $n$ women are to be seated in a row so that no two women sit together. If $m > n$, then the number of ways in which they can be seated, is

Explanation

Reviewed by Dr. Abubacker

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