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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. India’s #1 Learning Platform Start Complete Exam Preparation
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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
Non-Human User Joined: 09 Sep 2013 Posts: 24839
Re: Three married couples have bought 6 seats in a row for a [#permalink] Hello from the GMAT Club BumpBot!Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________
Re: Three married couples have bought 6 seats in a row for a [#permalink] 11 Dec 2018, 02:47
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Three married couple bought 6 seats in a row for a concert in how many ways can they be seated
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