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.
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
combination (tough)
This topic has expert replies
-
piyush_nitt
- Master | Next Rank: 500 Posts
- Posts: 424
- Joined: Sun Dec 07, 2008 5:15 pm
- Location: Sydney
- Thanked: 12 times
7C3*4C2*2C2 + 7C2*5C3*2C2 + 7C2*5C2*3C3 = 630mariah 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.
-
gaggleofgirls
- Master | Next Rank: 500 Posts
- Posts: 138
- Joined: Thu Jan 15, 2009 7:52 am
- Location: Steamboat Springs, CO
- Thanked: 15 times
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
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
