Question

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each.First the women choose the chairs from among the chairs marked 1 to 4, then the men select the chairs from among the remaining. The number of possible arrangements is

• A. ${}^4{P}_2{.}^6{P}_3$
• B. ${}^6{C}_3{.}^4{C}_2$
• C. ${}^4{C}_2{.}^4{P}_3$
• D. ${}^4{P}_2{.}^4{P}_3$

Answer 1

The correct option is A ${}^4{P}_2{.}^6{P}_3$

Firstly women will go and choose any two out of first four,So arrangement of 2 out 4 is ${}^4{P}_2$
And three men will choose out of 6,So arrangement of 3 out 6 is ${}^6{P}_3$
$\therefore$ required ways ${=}^4{P}_2{.}^6{P}_3$