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boys and girls

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by Deepthi Subbu » Wed Sep 28, 2011 5:57 am
In how many ways can 5 boys and 4 girls be arranged in a line so that there will be a boy at the
beginning and at the end?

1. 3! * 7! / 5!
2.5!*7!/6!
3.5!* 7!/3!
4.3!*7!/5!
5.5!*7!/7!
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by shankar.ashwin » Wed Sep 28, 2011 6:12 am
Any of the 5 boy can sit in the 1st position, and any of the remaining 4 can take the last..

5 _ _ _ _ _ _ _ 4

The other 7 positions can be filled in 7! ways.

So, it should be 5*4*7! ways.

This is 5!7!/3! C IMO
Last edited by shankar.ashwin on Wed Sep 28, 2011 6:21 am, edited 2 times in total.
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by user123321 » Wed Sep 28, 2011 6:15 am
arrange two boys at extreme positions in 5p2 ways
remaining three boys+4 girls can be arranged in remaining places in 7! ways
so ans = 5p2*7! = 5!7!/3!

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by Deepthi Subbu » Wed Sep 28, 2011 6:17 am
Its mentioned that no two boys are indistinguishable , meaning they are different, hence the confusion.
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by navami » Wed Sep 28, 2011 7:34 am
5!7!/3!

we should not consider combination case here ....
each individuals are diff..
This time no looking back!!!
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