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# If a class of 10 students has five men, how many ways can the men and

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Math Expert
Joined: 02 Sep 2009
Posts: 61283
If a class of 10 students has five men, how many ways can the men and  [#permalink]

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07 Nov 2019, 01:22
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Difficulty:

55% (hard)

Question Stats:

39% (01:08) correct 61% (01:30) wrong based on 49 sessions

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If a class of 10 students has five men, how many ways can the men and women be arranged in a circle so that no two men sit next to each other?

A. 5!4!
B. 5!5!
C. 4!4!
D. 10!
E. 10!/5!

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Re: If a class of 10 students has five men, how many ways can the men and  [#permalink]

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12 Nov 2019, 19:36
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Bunuel wrote:
If a class of 10 students has five men, how many ways can the men and women be arranged in a circle so that no two men sit next to each other?

A. 5!4!
B. 5!5!
C. 4!4!
D. 10!
E. 10!/5!

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If no two men sit next to each other, a man must sit between two women. Since there are an equal number of men and women, it must be true that no two women are sitting to each other also (because a woman must sit between two men also). In other words, the men and women sit alternately next to each other. Since we have a circular arrangement, we use the circular permutations formula, and so the number of ways to arrange the 5 men is (5 - 1)! = 4!. However, since there are 5 seats remaining, the number of ways to arrange the women is 5!. Thus, the total number of ways the men and women can be arranged in a circle so that men and women sit alternately next to each other is 4! x 5!.

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Re: If a class of 10 students has five men, how many ways can the men and  [#permalink]

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07 Nov 2019, 09:11
Bunuel wrote:
If a class of 10 students has five men, how many ways can the men and women be arranged in a circle so that no two men sit next to each other?

A. 5!4!
B. 5!5!
C. 4!4!
D. 10!
E. 10!/5!

Are You Up For the Challenge: 700 Level Questions

its a question of circular arrangement with condition that no two men sit next to each other or say that a woman sits b/w two men
so men 1st position is fixed and can be arranged in 4! ways and women be arranged in 5! ways
IMO A ; 5!4!
Re: If a class of 10 students has five men, how many ways can the men and   [#permalink] 07 Nov 2019, 09:11
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