30 students, 6 parents: number of 10-student groups, number

D

D!ddy

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Nov 2, 2007
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Hey, it's been awhile since I've been here but I'm back for help again :) It's a 2-part question.

#1. A ski trip at the school has been arranged. There are 30 students that have paid for the trip and 6 parents that have volunteered to chaperone. To transport the students and parents easily, they are to be divided into two groups. One group has 10 students and 2 parents, and the other group has 20 students and 4 parents.

A.How many different groups of 10 students can be formed? -So I did the question myself and came up with the answer 30,045,015 different ways. and I used combinations to solve this(30 nCr 6) and solved it for the product.

B. Mina is one of the students going on the ski trip, and Mina's mother volunteered to be one of the chaperons. Mina's mother would prefer to be in the smaller group and not in the same group as Mina. If this wish is honored, how many ways can the smaller group and its chaperone be chosen? - This question was kind of difficult but I started it off with (10 nCr 6), and solved it for the product, and came up with 210.



So I was just hoping you guys could please go through the question, and tell me if I was correct or not.

Thanks in Advance, Diddy
 
Re: Perm/Comb Question

D!ddy said:
#1. A ski trip at the school has been arranged. There are 30 students that have paid for the trip and 6 parents that have volunteered to chaperone. To transport the students and parents easily, they are to be divided into two groups. One group has 10 students and 2 parents, and the other group has 20 students and 4 parents.
B. Mina is one of the students going on the ski trip, and Mina's mother volunteered to be one of the chaperons. Mina's mother would prefer to be in the smaller group and not in the same group as Mina. If this wish is honored, how many ways can the smaller group and its chaperone be chosen?[/b] - This question was kind of difficult but I started it off with (10 nCr 6), and solved it for the product, and came up with 210.
Click to expand...

For B Mina mother is in the smaller group but not Mina.
\(\displaystyle {29 \choose 10}(5)=100150050\)
 
Re: Perm/Comb Question

Don't feel bad, Diddy; you're only out 100150050 - 210 = 100149840 :wink:

Plus your other solution is keereck :!:
 
Re: Perm/Comb Question

I hope you mean correct by keereck lol, but pka, is it 29 over 10 times 5? or is it 29! over 10!, where does the 5 come from?
 
Re: Perm/Comb Question

"29 over 10" as shown by pka is simply a way of saying 29C10 (29 Choose 10).
So it really means 29! / (10!19!).

Why does the 5 come in? There are 5 available parents : kapish?
 
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