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Doubt with two combination questions:

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by kaulnikhil » Sat Jun 27, 2009 10:36 pm
A group of 8 friends want to play doubles tennis. How many different ways can the group be divided into 4 teams of 2 people?
A. 420
B. 2520
C. 168
D. 90
E. 105
I understood it was previously discussed in this forum. However I got problem with the other question which goes as follows:
There are 12 girls and 15 boys.In how many ways we can form 4 pairs of boys and 4 pairs of girls for a dance .
1 12C4*15c4
2 12C4*15C4*8
3 12C4*15C4*4!
4 27C4*4

[spoiler]I thought the ans to be one as we have already considered various combinations resulting from the question . If the order of the groups had not been important we would have divided by 4!. As the order is already considered in 1. why do we have to multiply by 4! over here.[/spoiler]
Last edited by kaulnikhil on Sun Jun 28, 2009 10:47 am, edited 1 time in total.
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by dtwea » Sun Jun 28, 2009 3:27 am
If you want 4 pairs of girls from 12 girls, the first pair comes from 12, 2nd pair comes from 10 .....

(12C2 x 10C2 X 8C2 X 6C2)/4! ( (G1 G2) ( G3 G4) (G5 G6)( G7G8)=(G5 G6)( G7G8) (G1 G2) ( G3 G4) )
and that is why you divide by 4!

12C4 means forming a group of 4 girls from 12. Four girls are not 4 pairs of girls =8 girls so I don't know where those choices are going.

Using this logic to solve the first problem we have

(8C2 * 6C2 * 4C2 *2C2)/4!= 105
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by kaulnikhil » Sun Jun 28, 2009 3:53 am
The answer for the above post is 12C4*15C4*4! ....The explanation says selected boys and girls can be arranged in 4! ways
Last edited by kaulnikhil on Sun Jun 28, 2009 10:48 am, edited 1 time in total.
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by dtwea » Sun Jun 28, 2009 4:12 am
kaulnikhil wrote:The answer for the above post is 12C4*14C4*4! ....The explanation says selected boys and girls can be arranged in 4! ways
4 pairs of boys or 4 boys? If you mean 4 pairs of boys or girls, they have to explain 12C4. or 14C4.
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by ladhanivishal » Wed Jul 08, 2009 12:35 am
yeah doesnt look like "pairs" is correct.. secondly there is not arrangement or order.. it only says "how to form" so the answer should be A

Also if there was an arrangement.. it should have been multiplied by 8! and not 4!... can anybody throw some more light here..
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