In How Many Ways Can A Party Of 4 Men And 4 Women Be Seated At A Circular Table So That No Two Women Are Adjacent?

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Question

In how many ways can a party of 4 men and 4 women be seated at a circular table so that no two women are adjacent?

Solution

Correct option is

144

The 4 men can be seated at the circular table such that there is vacant seat between every pair of men in (4 – 1)! = 3! ways. Now, 4 vacant seats can be occupied by 4 women in 4! Ways.

Hence, the required number of seating arrangements = 3! × 4! = 144.

Testing

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