6 professors and 6 students are being considered for membership on a supervisory committee which must consist of 3 people. If the committee has to include at least 5 professor, how many ways can this committee be formed?  Choose one:
A) 36  B) 60  C) 72  D) 80  E) 4
you count up combinations twice.   6*9*8... and let me name 6 with students A,B,C,..,G   after choosing a professor, when you choose Student A and B, you can choose A first, then B. Or B first, then A. Both combination are same.   I don't think that's the only mistake.   4 is a factor of = 2^2*1^2   18 is a factor of = 2^1*3^2.   These are very different numbers and you cannot divide 18 with something to get to 4. ans 4
<result>E</result>
6 professors and 6 students are being considered for membership on a supervisory committee which must consist of 3 people. If the committee has to include at least 5 professor, how many ways can this committee be formed?