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Team Question

by sxk1693 » Sun Jan 20, 2013 1:14 pm

47. Mrs. Walker has 6 boys and 4 girls on her math team. How many different 4 person teams can be formed if her team has to have at least 1 boy and 1 girl.

HIGHS 2013 MEETS:
NS: 220(TMSCA STATE)
CA: 232(B)
MA: 274(District)
SC: 220(A)
CS: 212(VCM1)

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Re: Team Question

by darksaber21 » Sun Jan 20, 2013 1:27 pm

We are looking for the number of combinations, which is the number of permutations over the number of possible arrangements of one permutation, right? Well, if we need at least one boy and one girl, then we have 6 possibilities for one spot, and 4 for another. Then, it doesn't matter who obtains the other two seats, so 8 different possible people for the third, and 7 for the fourth (as two or three people have been chosen before choosing the third or fourth spot respectively). So, assuming I did the math right:

[unparseable or potentially dangerous latex formula]

Now I know the stakes, and I'm willing to show what I gots. I will see you all at state for the first and final time, so let's end the year with a bang! :)
MTHS - Class 5A, District VII, Region I

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Re: Team Question

by PokémonMaster » Sun Jan 20, 2013 1:49 pm

I actually think you add the separate combinations.

There are 24 3-girl 1-guy combinations , 90 2-girl 2-boy combinations, and 80 3-male 1-female combinations, which makes 194 total combinations.

UIL C 2013-14

NS: 298
Calculator: 240
Math: 282
Science: disheartening

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Re: Team Question

by 101dalmatians » Sun Jan 20, 2013 8:44 pm

I guess this signature really doesn't matter now that I know that the forum is going down soon...

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Re: Team Question

by darksaber21 » Sun Jan 20, 2013 9:00 pm

I'm probably wrong. I am bad at combinations....

But I would also like to know the answer, should I be wrong.

Now I know the stakes, and I'm willing to show what I gots. I will see you all at state for the first and final time, so let's end the year with a bang! :)
MTHS - Class 5A, District VII, Region I

darksaber21: Celebrated Spammer; Posts: 477; Joined: Tue May 29, 2012 6:20 pm; Location: Arlington, TX

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Re: Team Question

by 101dalmatians » Sun Jan 20, 2013 10:06 pm

But my thought was blanks probability ( I feel im wrong but these are my thoughts...):

So ->

At least one boy and one girl right?

[unparseable or potentially dangerous latex formula] (2 boys, 2 girls)

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula] (3 boys, 1 girl)

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula] (1 boy, 3 girls)

[unparseable or potentially dangerous latex formula]

Total: [unparseable or potentially dangerous latex formula] possibilities.

I guess this signature really doesn't matter now that I know that the forum is going down soon...

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Re: Team Question

by darksaber21 » Sun Jan 20, 2013 10:09 pm

The problem with that is that is total number of permutations. The question asks for the number of combinations.

So, since on group of four people can be arranged twenty-four different ways, we could divide the result by 24, but then our answer is 41 in that case... So I don't know...

Now I know the stakes, and I'm willing to show what I gots. I will see you all at state for the first and final time, so let's end the year with a bang! :)
MTHS - Class 5A, District VII, Region I

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Re: Team Question

by 101dalmatians » Sun Jan 20, 2013 10:12 pm

Oh... I see the mistake I did!
So is it like you divide by like [unparseable or potentially dangerous latex formula] in this kind of problem?
So if is groups of 3 then it would be [unparseable or potentially dangerous latex formula]?

I guess this signature really doesn't matter now that I know that the forum is going down soon...

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Re: Team Question

by sxk1693 » Mon Jan 21, 2013 1:52 pm

Oh yeah. Sorry about that. Pokemon Master is Right. 194 teams.

HIGHS 2013 MEETS:
NS: 220(TMSCA STATE)
CA: 232(B)
MA: 274(District)
SC: 220(A)
CS: 212(VCM1)

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Re: Team Question

by 101dalmatians » Mon Jan 21, 2013 5:19 pm

I guess this signature really doesn't matter now that I know that the forum is going down soon...

101dalmatians: Ubiquitous Spammer; Posts: 1013; Joined: Mon Aug 27, 2012 6:30 pm; Location: Dallas, Tx.

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Re: Team Question

by 007math » Tue Jan 22, 2013 9:51 am

Hehe, the Mrs. Walker this problem refers to is my coach :D

3rd Place State Mathematics 5A 2012

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