Eight men and eight women need to be seated around a circular table such that no two women sit next to each other. How many different arrangements can be made?

Answer Choices

Correct answer marked below

7!*8!

Correct

8!*8!

7!*9!

8!*9!

9!*9!

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Official Explanation

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To solve the problem of arranging 8 men and 8 women around a circular table with the condition that no two women are adjacent, we first arrange the 8 men in a circle. The number of ways to arrange n distinct objects in a circle is given by (n-1)!. Therefore, the men can be arranged in (8-1)! = 7! ways. Once the men are seated,…

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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.