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Find the number of ways in which 5 boys and 5 girls be seated in a row so that all the girls are never together.

Find the number of ways in which 5 boys and 5 girls be seated in a row so that all the girls are never together.

Grade:12

1 Answers

Satviki Pathak
40 Points
7 years ago
The answer is 10!-(6!5!). The total number of ways of arranging 5 boys and five girls is 10!. Now we consider the total number of ways of seating them such that the 5 girls are always together and we subtract this from 10!.
For that, Let us consider the 5 girls as 1 unit. Therefore total number of ways of seating 5 boys and the 1 unit =6!5! ( Multiplying by 5! as the five girls can be arranged amongst themselves in 5! ways), Thus, the answer is 10!-(6!5!)

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