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Given:
3 married couples have bought 6 seats in the same row for a talent show.
Formula used:
n! = n × (n – 1) × (n – 2) ……………………….3 × 2 × 1
Calculation:
The guys all sit first, but they have to take up 3 spaces.
Assuming we're dealing with male-female married couples here
The men have 3! ways of sitting, as do the women
Total=
⇒ 3! × 3!
⇒ (3!)2
⇒ (6)2
⇒ 36
∴Different ways can they be seated if all men sit together to the right of all women is 36.
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Manager
Joined: 14 Dec 2004
Posts: 74
Three married couples have bought 6 seats in a row for a [#permalink]
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?
Manager
Joined: 22 Jun 2004
Posts: 236
Location: Bangalore, India
Re: Three married couples have bought 6 seats in a row for a [#permalink]
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..
cloaked_vessel wrote:
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?
Senior Manager
Joined: 07 Jun 2004
Posts: 465
Location: PA
Re: Three married couples have bought 6 seats in a row for a [#permalink]
1. 6! 2. 3! 3. 3! * (2!)^3
4. 3! * 3! * 2!
Manager
Joined: 14 Dec 2004
Posts: 74
Re: Three married couples have bought 6 seats in a row for a [#permalink]
correct answers:720,6,48,
72
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Joined: 09 Sep 2013
Posts: 24839
Re: Three married couples have bought 6 seats in a row for a [#permalink]
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Re: Three married couples have bought 6 seats in a row for a [#permalink]
11 Dec 2018, 02:47
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