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sam_08855
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A professor will assign seven projects to three students. If 20 Oct 2006, 00:02
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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?

I will post the OA after some expls are posted.



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SimaQ
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A professor will assign seven projects to three students. If 20 Oct 2006, 00:09
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Ok, this is my weak point...

Number of ways to select 2 projects out of 7: 7C2=21
Number of ways to select 3 projects out of 7: 7C3=35

2*21+35=77....

ok, now somebody show us the correct answer? :)
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keeeeeekse
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A professor will assign seven projects to three students. If 20 Oct 2006, 06:27
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at first try i got 210, am i totally off???

7C2 for the first student, 5C2 for the second and 3C3 to the third

so 21*10*1=210
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londonluddite
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A professor will assign seven projects to three students. If 20 Oct 2006, 10:58
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Got 210 too

ways of selecting 4 projects from 7 = 7C4 = 35
way of assigning 4 projects to 2 people = 4C2 = 6

last 3 go to one person so no multiplier = 35 * 6 = 210
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mst
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A professor will assign seven projects to three students. If 20 Oct 2006, 11:27
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Let the 3 students be A, B and C. There are 3 ways in which the projects can be distributed: A gets 3, B &C get 2 projects. B gets 3, A &C get 2. C gets 3, A&B get 2.

The 7 projects can be chosen as follows: 7C2 x 5C2 x 3C3 = 210.
Do we also need to take into consideration the 3 arrangements that are possible: 210 x 3= 630

What is the OA?
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sam_08855
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A professor will assign seven projects to three students. If 20 Oct 2006, 14:21
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mst got it right as per OA

My question is - shouldn't there be 3! = 6 ways of allocating the 3,2,2 project "bundles" to 3 students? In other words,

A = bundle 1 of 2 projects
B = Bundle 2 of 2 projects

and

vice versa

are 2 different allocations.



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Hi there,
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