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combination (tough)

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by mariah » Fri Feb 06, 2009 5:14 pm
A professor will assign seven projects to three students. If two students each got 2 projects, and the other one got 3 projects, how many ways are possible?

oa is 630
my answer - 7C2*5C2*3C3=210
please explain.
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Re: combination (tough)

by piyush_nitt » Fri Feb 06, 2009 7:54 pm
mariah wrote:A professor will assign seven projects to three students. If two students each got 2 projects, and the other one got 3 projects, how many ways are possible?

oa is 630
my answer - 7C2*5C2*3C3=210
please explain.
7C3*4C2*2C2 + 7C2*5C3*2C2 + 7C2*5C2*3C3 = 630
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by gaggleofgirls » Fri Feb 06, 2009 7:59 pm
To add a little explanation. Notice that the correct answer is 3 times the answer you got. That is becuase you chose to have the professor assign 2 projects to student A, then two projects to student B then the remaining 3 to Student C.

But there are two other ways the professor can assign the projects:

First 3 to Student A, then 2 to Student B then the remaining 2 to student C
and
First 2 to student A then 3 to student B and the remaining 2 to student C.

This gives us the 3 equations to add together.

7C2 * 5C2 *3C3

7C3 * 4C2 *2C2

7C2 * 5C3 * 2C2

Each one of them gives 210 combinations for a total of630 combinations.

-Carrie
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