Four boys and four girls are to be seated around a circular table. In how many different ways can they be arranged so that no two girls sit next to each other?
Answer and explanation
Correct answer: D.
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To prevent any two girls from sitting adjacent to each other, each girl must occupy one of these distinct available spaces.
The number of linear ways to arrange the 4 girls into these distinct spaces is .
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To prevent any two girls from sitting adjacent to each other, each girl must occupy one of these distinct available spaces.
The number of linear ways to arrange the 4 girls into these distinct spaces is .
.
- Step 1: First arrange the 4 boys around the circular table. The number of circular permutations of distinct objects is :
- Step 2: Seating the 4 boys creates distinct spaces between them around the table.
- Step 3: Multiply the possibilities by the multiplication rule of counting :
Answer
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