Permutations and Combinations
Circular Permutations
Premium Question
Grade 11
Question:
The number of ways in which $4$ boys and $4$ girls can be seated around a circular table so that boys and girls alternate is:
(1) $24$
(2) $72$
(3) $144$
(4) $288$
Step-by-Step Solution
Key Concept: Fix one boy (circular permutation): $(4 - 1)! = 6$ arrangements for boys. Girls fill the 4 gaps between boys: $4! = 24$ ways. Total $= 6 \times 24 = 144$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)