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There are 11 chairs in a row. There are 3 boys and 5 girls. Find the number of arrangements such that no 2 boys sit together-

There are 11 chairs in a row. There are 3 boys and 5 girls. Find the number of arrangements such that no 2 boys sit together-

Grade:11

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
5 years ago
First we arrange the boys. we remove 3 chairs
there are 9 gaps in the 8 remaining chairs where the 3 chairs of the boys can be arranged in ^9C_3.3! ways

then the remaining girls can be arranged in
^8C_5.5!
so the total number of ways is
^8C_5.5! \times ^9C_3.3!

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