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13 Jan 2005, 20:09
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Three married couples have bought 6 seats in a row for a performance of a musical comedy.
1. In how many ways can they be seated?
2. In how many ways can they be seated if each couple is to sit together with the husband to the left of the wife?
3. In how many ways can they be seated if each couple is to sit together?
4. In how many ways can they be seated if all the men are to sit together and all the women are to sit together?
1. In how many ways can they be seated?
2. In how many ways can they be seated if each couple is to sit together with the husband to the left of the wife?
3. In how many ways can they be seated if each couple is to sit together?
4. In how many ways can they be seated if all the men are to sit together and all the women are to sit together?
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14 Jan 2005, 00:28
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Here are my answers.
(1) 6 people in 6 seats => 6! = 720
(2)There is a definite order contsraint that husband is to the left of wife. Thus, 3 couples can seat in 3! = 6 ways.
(3)3 couples can seat in 3! ways and each couple can themselves change seats in 2! ways.
Thus, the totall number of ways = 3! * 2! *2! * 2! = 48
(4)3 Men can seat 3! ways in 3 seats.
3 Women can seat 3! ways in 3 seats.
Men and women as two packs can occupy the seats in 2! ways (Leftmost 3 seats women or rightmost 3 seats women).
=> the total number of ways = 2! * 3! * 3! = 72
Awaiting answers..
(1) 6 people in 6 seats => 6! = 720
(2)There is a definite order contsraint that husband is to the left of wife. Thus, 3 couples can seat in 3! = 6 ways.
(3)3 couples can seat in 3! ways and each couple can themselves change seats in 2! ways.
Thus, the totall number of ways = 3! * 2! *2! * 2! = 48
(4)3 Men can seat 3! ways in 3 seats.
3 Women can seat 3! ways in 3 seats.
Men and women as two packs can occupy the seats in 2! ways (Leftmost 3 seats women or rightmost 3 seats women).
=> the total number of ways = 2! * 3! * 3! = 72
Awaiting answers..
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