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Team Question
Posted:
Sun Jan 20, 2013 1:14 pmby sxk1693
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.
Re: Team Question
Posted:
Sun Jan 20, 2013 1:27 pmby darksaber21
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]
Re: Team Question
Posted:
Sun Jan 20, 2013 1:49 pmby PokémonMaster
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.
Re: Team Question
Posted:
Sun Jan 20, 2013 8:44 pmby 101dalmatians
Re: Team Question
Posted:
Sun Jan 20, 2013 9:00 pmby darksaber21
I'm probably wrong. I am bad at combinations....
But I would also like to know the answer, should I be wrong.
Re: Team Question
Posted:
Sun Jan 20, 2013 10:06 pmby 101dalmatians
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.
Re: Team Question
Posted:
Sun Jan 20, 2013 10:09 pmby darksaber21
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...
Re: Team Question
Posted:
Sun Jan 20, 2013 10:12 pmby 101dalmatians
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]?
Re: Team Question
Posted:
Mon Jan 21, 2013 1:52 pmby sxk1693
Oh yeah. Sorry about that. Pokemon Master is Right. 194 teams.
Re: Team Question
Posted:
Mon Jan 21, 2013 5:19 pmby 101dalmatians
Re: Team Question
Posted:
Tue Jan 22, 2013 9:51 amby 007math
Hehe, the Mrs. Walker this problem refers to is my coach :D