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In how many ways can four girls and three boys be arranged in a row so
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29 Sep 2021, 04:19
29 Sep 2021, 04:19
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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
А. 180
B. 360
C. 540
D. 720
E. 1440
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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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29 Sep 2021, 05:14
29 Sep 2021, 05:14
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Carcass 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
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 GRE. So, be sure to learn it.
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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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15 Aug 2024, 02:47
15 Aug 2024, 02:47
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