In how many ways can 5 boys and 3 women be arranged in a circle if the

Question

In how many ways can 5 boys and 3 women be arranged in a circle if the women are always to stand together ? (2 seating arrangements are considered different only when the positions of the people are different relative to each other.)

A. 120
B. 720
C. 1080
D. 1440
E. 4320

A. 120
B. 720
C. 1080
D. 1440
E. 4320

CrackverbalGMAT · Answer

The number of permutations of n things in a circle, when clockwise and anti clockwise are considered to be different is = (n - 1)!

Let us consider the 3 women as 1 unit. So we have 6 units (5 boys + 1 unit of 3 women) to arrange.

External arrangement = (6 - 1)! = 5! = 120

Internal arrangement of the women = 3! = 6

Total number of ways = 120 * 6 = 720

Option B

Arun Kumar

anonymous19 · Answer

If I am wrong please explain. Thank you.

My Calculation:

Suppose 3 women as 1. The total becomes 6 people(5 boys + 1):

Based on 6 people, the total arrangement possible = 6! = 720

Now, Internal arrangement of the women = 3! = 6

Total number of ways = 720 * 6 = 4320, therefore, my answer is E.

CrackverbalGMAT · Answer

hi anonymous19...we have to arrange them in a circle. so the 6 units have to be arranged as (6 - 1)! = 5! = 120

Hope this helps

Arun Kumar

ScottTargetTestPrep · Answer

Solution:
 
Recall that the number of arrangements of n objects in a circular fashion is (n - 1)!. So if there are no restrictions, the 8 people can be seated in (8 - 1)! = 7! different ways. However, since the three women have to sit together, they can be considered as 1 “entity” person. In other words, we can treat the situation as if there are only 6 people (the 1 “entity” person and the 5 boys), and hence there are (6 - 1)! = 5! seating arrangements. However, since the three women can be seated in 3! ways, there are a total of 5! x 3! = 120 x 6 = 720 different seating arrangements.

Answer: B

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In how many ways can 5 boys and 3 women be arranged in a circle if the

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In how many ways can 5 boys and 3 women be arranged in a circle if the

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