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_3 xx ""^4C_2`
b. `""^4P_2 xx ""^4P_3`
c. `""^4C_2 xx ""^4P_3`
d. none of these

Explanation

First women choose the chairs from amongst the chairs 1 to 4.
Two women can be arranged in 4 chairs in `.^(4)P_(2)` ways.
In remaining 6 chairs 3 men can be arranged in `.^(6)P_(3)` ways.
`therefore` Total number of possible arrangements `= .^(4)P_(2)xx .^(6)P_(3)`
`=(4!)/(2!)xx(6!)/(3!)` ltbgt `=4xx3xx6xx5xx4`
=1440.