Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A three-person committee must be chosen from a group of 7 [#permalink]
18 Jan 2006, 19:20

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct
0% (00:00) wrong based on 2 sessions

A three-person committee must be chosen from a group of 7 professors and 10 graduate students. If at least one of the people on the committee must be a professor, how many different groups of people could be chosen for the committee?

A. 70
B. 560
C. 630
D. 1,260
E. 1,980

Plz, help me out with this, guys.

My solution: C(7;1)*C(16;2)=7*120=840
What's wrong with my reasoning here. _________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

Re: combination problem PS [#permalink]
30 Aug 2007, 13:19

rlevochkin wrote:

A three-person committee must be chosen from a group of 7 professors and 10 graduate students. If at least one of the people on the committee must be a professor, how many different groups of people could be chosen for the committee?

A. 70 B. 560 C. 630 D. 1,260 E. 1,980

Plz, help me out with this, guys.

My solution: C(7;1)*C(16;2)=7*120=840 What's wrong with my reasoning here.

many posted the right solution here, which is 560. but could some permutation / combination expert please explain why the solution proposed above: C(7;1)*C(16;2)=7*120=840 is not applicable here?? i cant find an explanation...

thanks a lot

EDIT:

with the help of my little sister i found the flaw myself... the problem is when you select 2 out of 16, i.e. C(16;2) then these two guys might be two professors or one professor and you cannot multiply them with 7 (the #professors) since only 5 or 6 professors would be left. therefore, as the correct solution suggest, you have differentiate between the scenarios 1prof/2studs, 2profs/1stud, 3profs.

Last edited by skkingdom on 30 Aug 2007, 13:49, edited 1 time in total.

Re: combination problem PS [#permalink]
30 Aug 2007, 13:47

skkingdom wrote:

many posted the right solution here, which is 560. but could some permutation / combination expert please explain why the solution proposed above: C(7;1)*C(16;2)=7*120=840 is not applicable here?? i cant find an explanation...

thanks a lot

not so sure, but this how i understand it. you are trying to multiply the probabilities of choosing from the two overlaping sets. so you have many duplicates.

Re: combination problem PS [#permalink]
30 Aug 2007, 13:51

ankita wrote:

skkingdom wrote:

many posted the right solution here, which is 560. but could some permutation / combination expert please explain why the solution proposed above: C(7;1)*C(16;2)=7*120=840 is not applicable here?? i cant find an explanation...

thanks a lot

not so sure, but this how i understand it. you are trying to multiply the probabilities of choosing from the two overlaping sets. so you have many duplicates.

i think i just edited above at the same time you answered yes you are right, there is a considerable overlap, that makes the 840 possibilities incorrect

gmatclubot

Re: combination problem PS
[#permalink]
30 Aug 2007, 13:51