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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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donatchange | Student, Grade 11 | (Level 2) eNoter

Posted June 10, 2013 at 12:43 PM via web

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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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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted June 10, 2013 at 12:56 PM (Answer #1)

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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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