Question

In how many ways can 5 boys and 5 girls be seated at a round table so that no two girls may be together?

• A. \( 4! \)
• B. \( 4! \times 5! \)
• C. \( 5! \)
• D. \( 5! \times 4! \)

Hint:

In circular arrangements, fix one element in place to remove equivalent arrangements due to rotation.

Answer 1

The Correct Option is D

Step 1: Fix one boy at the round table.
Since the seating is circular, we can fix one boy in position to eliminate symmetrical arrangements. We then arrange the remaining 4 boys, which can be done in \( 4! \) ways.
Step 2: Arrange the girls.
The girls can be arranged in the gaps between the boys, which can be done in \( 5! \) ways.
Step 3: Conclusion.
Thus, the total number of ways to arrange the boys and girls is \( 5! \times 4! \). Final Answer: \[ \boxed{5! \times 4!} \]