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In how many ways can 7 men and 7 women sit on a round table such that no two women sit together?

(a) 2(7 !) 

(b) (6 !)2 

(c) 7 ! × 6 ! 

(d) (7 !)2

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Best answer

(c) 6! × 7!

7 men can seat themselves in a round table in (7 – 1)! = 6! ways. 

Now there are 7 places vacant between these 7 men. 

∴ 7 women can seat themselves in these 7 places in 7 ! ways. 

∴ Total number of required arrangement where no two women sit together = 6! × 7!.

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