5 girls and 5 boys are to be seated around a circular table such that no two girls are together. Find the number of ways to be seated.

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Solution

5 boys can sit around the circular table in (5–1)! = 4! ways

For boys and girls to occupy alternate positions, 5 girls has to sit in the gap between the 5 boys.

The girls can be arranged in these gaps in 5! ways

Therefore, total number of seating arrangements = 4! * 5! = 24 * 120 = 2880

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5 girls and 5 boys are to be seated around a circular table such that no two girls are together. Find the number of ways to be seated.

5 boys can sit around the circular table in (5–1)! = 4! ways For boys and girls to occupy alternate positions, 5 girls has to sit in the gap between the 5 boys. The girls can be arranged in these gaps in 5! ways Therefore, total number of seating arrangements = 4! * 5! = 24 * 120 = 2880

5 boys can sit around the circular table in (5–1)! = 4! ways

For boys and girls to occupy alternate positions, 5 girls has to sit in the gap between the 5 boys.

The girls can be arranged in these gaps in 5! ways

Therefore, total number of seating arrangements = 4! * 5! = 24 * 120 = 2880