Eight chairs are numbered 1 to 8 . Two women and three men wish to occupy one chair each. First the women…
Eight chairs are numbered 1 to 8 . Two women and three men wish to occupy one chair each. First the women choose chairs from amongst the chairs marked 1 to 4 , and then the men select the chairs from amongst the remaining. The number of possible arrangements is
${ }^6 \mathrm{C}_3 \times{ }^4 \mathrm{C}_2$
${ }^4 \mathrm{P}_2 \times{ }^6 \mathrm{P}_3$
${ }^4 \dot{C}_2+{ }^4 \mathrm{P}_3$
${ }^4 \mathrm{P}_2+{ }^6 \mathrm{P}_3$
Solution
Two women can be made to sit on chairs marked 1 to 4 in ${ }^4 P_2$ ways and then three men can be seated in 6 available seats in ${ }^6 \mathrm{P}_3$ ways.
$\therefore \quad$ number of possible arrangements is ${ }^4 \mathrm{P}_2 \times{ }^6 \mathrm{P}_3$.