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5 Feb 2012 16:20:24 IST

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

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Vishal U. Karve

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5 Feb 2012 18:45:22 IST

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It is 10!-6!5!

shivansh shrivastava

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5 Feb 2012 21:22:03 IST

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Why 6!5! ?? :(

Vishal U. Karve

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6 Feb 2012 19:19:50 IST

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To find the ways in which all the girls are never together, we find the ways in which they are together and subtract it from total ways.

No. of ways in which they are together:

Let us suppose the boys are named B₁,B₂,B₃,B₄,B₅.

You know how to arrange six objects right? (In 6! ways..)

The six objects we have are- B₁, B_2, B_3, B_4, B_5, (girls).

[ The girls are all together, remember? So they are one unit ]

Now, in each of these 6! arrangements, the girls can be further arranged among themselves in 5! ways.

That gives 6!.5!.

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