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In how many ways can 7 gentlemen and 5 ladies be arranged in a circle if no two ladies are together.

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In how many ways can 7 gentlemen and 5 ladies be arranged in a circle if no two ladies are together.

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Ladies have to be arranged between gentlemen. The 7 gentlemen can be seated in 6! Ways. There are 7 gaps between the men which the 5 ladies can occupy in 7P5, ways. 

∴ The number of ways is 7P6.6!.

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