How many different ways can 6 men and 6 women arrange themselves around a circular table such that no two individuals of the same gender are adjacent?

Answer Choices

Correct answer marked below

5!5!

5!6!/2

5!6!

Correct

6!6!

11!

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Explanation

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Official Explanation

Official

To determine the number of arrangements of n distinct objects in a circle, we use the formula (n-1)!. For the 6 men, they can be arranged in (6-1)! = 5!. We can then position the 6 women in the gaps…

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What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.