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# This was posted in the "Share your experience" forum:

Author Message
Manager
Joined: 10 Jun 2003
Posts: 210
Location: Maryland

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21 Aug 2003, 10:07
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

This was posted in the "Share your experience" forum:

--------------------------------
There are 10 professor and 7 graduate students in group. How many way can you make a group of 3 if at least one professor must be in the group?

The answer is the sum of all of the followng which should be 560.

ppp = (10*9*8)/3!

ppg = (10*9*7)/2!

pgg = (10*7*6)/2!
---------------------------------

I believe the correct answer is 645. Can others confirm?

My method is the following:

For PGG: 10C1 * 7C2 = 10 * 21 =210
For PPG: 10C2 * 7C1 = 45 * 7 = 315
For PPP: 10C3 = 120

Add these up and you get 645.
Manager
Joined: 02 Jul 2003
Posts: 58

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21 Aug 2003, 10:56
I got the same

1pro +2 students=210
2pro+1 student=315
my 10C3 for three pro.

rich
Manager
Joined: 10 Jun 2003
Posts: 210
Location: Maryland

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21 Aug 2003, 11:05
rich28 wrote:
I got the same

1pro +2 students=210
2pro+1 student=315
my 10C3 for three pro.

rich

10C3 = (10*9*8)/(3*2) = 720/6 = 120
Intern
Joined: 20 Aug 2003
Posts: 36
Location: USA

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21 Aug 2003, 21:05
Hi,

I got 645 too..

the way I solved this problem was to take the combinations where there would be no professors in the group and subtract it from the total no. of combinations-

17C3=680-total comb

7C3=35-no prof at all

680-35=645
GMAT Instructor
Joined: 07 Jul 2003
Posts: 770
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE

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21 Aug 2003, 21:15
p_malh wrote:
Hi,

I got 645 too..

the way I solved this problem was to take the combinations where there would be no professors in the group and subtract it from the total no. of combinations-

17C3=680-total comb

7C3=35-no prof at all

680-35=645

Good job. Always look for "complements" to save you lots of time. The GMAT does this a lot.
_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

21 Aug 2003, 21:15
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