4 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 2 professor, how many ways can this committee be formed?	Choose the correct choice from the following.
A) 36 B) 64 C) 72 D) 80 E) 100
you count up combinations twice.   4*9*8... and let me name 6 with students A,B,C,..,F   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.   64 is a factor of = 2^2*4^2   144 is a factor of = 2^4*3^2.   These are very different numbers and you cannot divide 144 with something to get to 64.
<result>B</result>
4 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 2 professor, how many ways can this committee be formed?