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7 boys and 3 girls are to be seated in a row. How to calculate the number of ways they...

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7 boys and 3 girls are to be seated in a row. How to calculate the number of ways they can be seated if the 3 girls want to be seated together?

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We have 7 boys and three girls.

But 3 girls should sit together always. So the girls can be taken as one unit.

So now we have 7 boys and 1 unit of girl. Altogether it is 8.

So the ways that can arrange 8 people is 8!.

But we can interchange the positions of three girls while maintaining them together. So arranging three girls can be done in 3! ways.

 

So the ways that can arrange boys and girls are `8!xx3! = 241920`

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