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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.
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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-
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.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.