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Eight chairs are numbered 1 to 8. Two wo...

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

Text Solution

Verified by Experts

The correct Answer is:
468000
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.
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