I understand that the normal way to solve it would be 17C3 - 10C3 but can anyone shed light on why the other way doesn't work??
OK you are assuming 17C3 is picking total 3 people from a pack of 17
Who knows if the selected 3 are graduate students from the total profs and graduate students. It doesn't matter because we are simply looking at the number of total combinations - number of combinations we are not interested in.
Then your 10C3 is worng 'cos the number of graduate students to be removed are now not 10 but 7
is wrong (This actually gives the correct answer and is the suggested method)
Like wise of the 3 selected from 17 , 2 are graduate student and 1 prof you have only 8 graduate students out of whom you have to select 3 which is again wrong.
This is getting worse!
Firstly 17C3 - 10C3 = 560 (The correct answer
) and is also the suggested method from the combinations course on this website --- see:
http://www.gmatclub.com/content/courses ... ations.php
This method makes sense - you are finding the total number of ways of choosing 3 people from 17 and then subtracting the total number of ways of choosing a committee of 3 from 10 students alone.
However - this is fine and is NOT
what the post was querying at all!!!!!!!!
The question is - what is wrong with the following method?:
We have to have at least 1 professor so we have 7 choices: 7
Next we can choose any one member from a group of 16, so 16 choices: 16
Finally we can choose any one member from a group of 15 - so 15 choices: 15
7*16*15 = 1680
Order not important so 1680/3*2*1 = 280 (because no. of ways to permute 3 people is 3*2*1)
Why doesn't this yield the correct answer?