Question

8 chairs are numbered from 1 to 8. Two women & 3 men wish to occupy one chair each. First, the women choose the chairs from amongst the chairs marked 1 to 4, then the men select the chairs from among the remaining. The number of possible arrangements is

• A. ${}^8{C}_3.{}^4{C}_4$
• B. ${}^4{P}_2.{}^4{P}_3$
• C. ${}^4{C}_3.{}^4{P}_3$
• D. ${}^4{P}_2.{}^6{P}_3$

Answer 1

Answer: (D)

${}^4{P}_2.{}^6{P}_3$

First the $2$ women can select any chair of the $4$ chairs numbered $1to4$ in ${}^4{P}_2$ ways
Then there will be $8-2=6$ chairs remaining, the $3$ men can select any chair of the $6$ chairs in ${}^6{P}_3$ ways
So, total number of ways $={}^4{P}_2\times {}^6{P}_3$ ways