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