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# There are 12 girls and 15 boys in a class.In how many ways

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Intern
Joined: 14 Nov 2004
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There are 12 girls and 15 boys in a class.In how many ways [#permalink]  02 Jun 2005, 09:56
There are 12 girls and 15 boys in a class.In how many ways can we form 4 pairs for a dance?

Thanks
Senior Manager
Joined: 15 Mar 2005
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Re: Combinations [#permalink]  02 Jun 2005, 10:37
If only a girl and a guy can pair up for a dance, then
12x15 + 11x14 + 10x13 + 9x12 = 180 + 154 + 130 + 108 = 572
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Director
Joined: 18 Apr 2005
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Re: Combinations [#permalink]  02 Jun 2005, 12:35
There are 12 girls and 15 boys in a class.In how many ways can we form 4 pairs for a dance?

Thanks

let's see

(12c4)(15c4)*4!
Intern
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Re: Combinations [#permalink]  02 Jun 2005, 13:30
sparky wrote:
There are 12 girls and 15 boys in a class.In how many ways can we form 4 pairs for a dance?

Thanks

let's see

(12c4)(15c4)*4!

sparky, why to multiply with 4!? Isn't it just (12C4)*(15C4)
Director
Joined: 18 Apr 2005
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Location: Canuckland
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Re: Combinations [#permalink]  02 Jun 2005, 13:36
emilem wrote:
sparky wrote:
There are 12 girls and 15 boys in a class.In how many ways can we form 4 pairs for a dance?

Thanks

let's see

(12c4)(15c4)*4!

sparky, why to multiply with 4!? Isn't it just (12C4)*(15C4)

emilem, i am not sure it's correct but the idea is you first pick 4 boys and 4 girls, not ordered. Then you line up, say, all the girls in any particular order and start arranging the boys and matching them with preordered girls - so 4! for boys.
VP
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Re: Combinations [#permalink]  02 Jun 2005, 13:46
emilem wrote:
sparky wrote:
There are 12 girls and 15 boys in a class.In how many ways can we form 4 pairs for a dance?

Thanks

let's see

(12c4)(15c4)*4!

sparky, why to multiply with 4!? Isn't it just (12C4)*(15C4)

you multiply by 4! to count the different ways to arrange the pairs. it is (12C4)*(15C4) to count the ways to choose the boys/girls from their respective groups. we have 4 spaces for 4 pairs. 1st space is 4 ways, 2nd space is 3 ways and so on...
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Senior Manager
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Re: Combinations [#permalink]  02 Jun 2005, 18:52
kapslock wrote:
If only a girl and a guy can pair up for a dance, then
12x15 + 11x14 + 10x13 + 9x12 = 180 + 154 + 130 + 108 = 572

Good solution kaps !

HMTG.
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Re: Combinations [#permalink]  02 Jun 2005, 21:19
HowManyToGo wrote:
kapslock wrote:
If only a girl and a guy can pair up for a dance, then
12x15 + 11x14 + 10x13 + 9x12 = 180 + 154 + 130 + 108 = 572

Good solution kaps !

HMTG.

Don't think this is correct though.
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Re: Combinations   [#permalink] 02 Jun 2005, 21:19
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