In how many ways can 7 boys and 7 girls be seated in a circle, such that no two girls are together?

2,188

CASE I: Consider the circular table case. Let's seat the seven girls first. The girls can be lined up in 7! ways and the table can be rotated in 7 ways so we can seat the girls in 7!/7 = 6! = 720 ways. There are 7 spaces between the girls so the boys can be arranged in 7! ways so the answer is 6!*7!. CASE II: Consider the straight line case. Let's seat the boys first where they can be arranged in 7! ways. Girls can sit in between or besides them such that maximum one girl is between any 2 boys as $$\text{1 B 2 B 3 B 4 B 5 B 6 B 7 B 8}$$ Clearly there are 8 places for the girls and hence the ways of arranging are 8C7=8 ways and the girls can be arranged in 7! ways, also the boys can be arranged in 7! ways so the answer is 8*7!*7!.

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Shivam
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Shivam

Updated on November 02, 2020

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  • Shivam
    Shivam about 3 years

    And also, the comparison of the same number of condition of people, but in a straight line , please ?