It is required to seat 5 men and 4 women in a row so that the men occupy odd places. Then the number of…
It is required to seat 5 men and 4 women in a row so that the men occupy odd places. Then the number of arrangements that are possible is
$144$
$362880$
$2880$
$1140$
Solution
$\frac{M}{1} \frac{W}{2} \frac{M}{3} \frac{W}{4} \frac{M}{5} \frac{W}{6} \frac{M}{7} \frac{W}{8} \frac{M}{9}$
5 men can be seated in 5 odd places in $5_{\mathrm{P}_5}=120$ ways and 4 women can be seated in remaining 4 places in $4_{p_4}=24$ ways $\Rightarrow$ Total possible arrangements $=120 \times 24=2880$