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

Question

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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Archit3110 · Answer

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!

ScottTargetTestPrep · Answer

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!.

Answer: A

metalhead2593 · Answer

Formula for ways of arranging n objects to a circle: n!/n = (n-1)!
So ways of arranging man are 4!
With the order is now fixated, there are 05 spaces for the women to squeeze in. So 5! ways of arranging women.

IMO 4!*5!. A

Thekingmaker · Answer

The way of cracking the nut is simple first we arrange the women in 5! ways and the rest of the men in placed in 4! ways as it;s circle one slot the front and back orders are arranged in a singlr way hence 4! amd IMO A

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

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

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