Question

It is required to seat $5$ men and $4$ women in a row so that the woman occupy the even places. How many such agreements are possible ?

Answer 1

total number of people $9$.

women occupy only even places women can occupy only four even places

$M\underset{–}{W}M\underset{–}{W}M\underset{–}{W}M\underset{–}{W}M$

$4$ women can sit in $4$ positions

$\therefore$ total no. of ways $={{}^{4}P}_4$

$\frac{4!}{(4-4)!}$

$=24$ ways

$5$ men can sit in $5$ positions

$\therefore$ total no. of ways $={{}^{5}P}_5$

$\frac{5!}{(5-5)!}$s

$\therefore$ total no. of agreements $=24\times 120$

$=2880ways$