There are 5 gentlemen and 4 ladies to dine at a round table. The number of ways in which they can seat themselves so that no two ladies are together, is

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There are 5 gentlemen and 4 ladies to dine at a round table. The number of ways in which they can seat themselves so that no two ladies are together, is

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2880

576

1440

480

answer is A.

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Detailed Solution

Five gentlemen can be seated at a round table in $(5 - 1)! = 4!$ ways. Now, 5 places are created in which 4 ladies can be arranged in $^{5} P_{4}$ ways

Hence, the total number of ways in which no two ladies sit togethar $= 4! \times^{5} P_{4} = 4! \times 5! = 2880$