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Re: In how many ways can four girls and three boys be arranged in a row so
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02 Mar 2021, 06:47
Expert Reply
Bunuel wrote:
In how many ways can four girls and three boys be arranged in a row so that the boys are always together ?
А. 180 B. 360 C. 540 D. 720 E. 1440
Make all boys as one group and treat the group as one individual
Now we have 1 Group and 4 girls who can be arranged in a row in 5*4*3*2*1 = 5! = 120 ways
But the boys can be arranged within the group in 3*2*1 = 3! = 6 ways
Total arrangements = 120*6 = 720
Answer: Option D
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Re: In how many ways can four girls and three boys be arranged in a row so
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02 Mar 2021, 06:48
2
Kudos
Expert Reply
Top Contributor
Bunuel wrote:
In how many ways can four girls and three boys be arranged in a row so that the boys are always together ?
А. 180 B. 360 C. 540 D. 720 E. 1440
Take the task of seating the 7 children and break it into stages.
We’ll begin with the most restrictive stage.
Stage 1: Arrange the three boys so that they are together We can arrange n unique objects in n! ways. So we can arrange the three boys together in 3! (6 ways)
Once we've arranged the three boys together, we'll "glue" them in place (to ensure they'll always be together)
Stage 2: Arrange the 5 entities (the 4 girls and the 3-boy entity) We can arrange these five unique objects in 5! ways (120 ways)
By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus seat all 7 children) in (6)(120) ways (= 720 ways)
Answer: D
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.
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