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 amongst the chairs marked 1 to 4, and then the men select th chairs from amongst the remaining. The number of possible arrangements is a.`^6C_3xx^4C_2` b. `^4P_2xx^4P_3` c. `^4C_2xx^4P_3` d. none of these

Explanation

First women choose the chairs from among 1 to 4 chairs. i.e., total number of chairs is 4. Since, there are two women, so number of arrangements = `""^(4)P_(2)` ways.
Now, men have to choose chairs from remaining 6 chairs.
Since, there are 3 men, so number can be arranged in `""^(6)P_(3)` ways.
`therefore" "` Total number of possible arrangements `= ""^(4)P_(2) xx ""^(6)P_(3)`
`= (4"!")/(4 - 2"!") xx (6"!")/(6 - 3"!")`
`= (4"!")/(2"!") xx (6"!")/(3"!")`
`(4 xx 3 xx 2"!")/(2"!") xx (6 xx 5 xx 4 xx 3"!")/(3"!")`
`= 4 xx 3 xx 6 xx 5 xx 4 = 1440`