Help with this question did I do this correctly? Could someone explain to me why I could use (7,4) did I do that right or should it be (7,3)? Please explain to me how i got this wrong if i did. A guy is looking for 5 members of his dissertation committee. It is required that the chair of the dissertation committee must be a mathematician. there are 3 professors in the mathematician department and 5 professors in the physics department. The chair must come from the mathematician department: there are 3 choices. The other four come from the remaining 7. Therefore the combinations would be C(7,4) I believe we would use this formula which is…. C(N,R) = N!/R!*(N-R)!) = N(N-1)(N-2)…(N-R+1)/R! C(7,4) = 7!/(4!*3!) = [(7*6*5*4)/(4*3*2*1)] = 35 So for reach 3 choices for the chair there are 35 choices for the rest of the committee. So 3*35 = 105 total combinations. Or we could do it like (3)7!/(4!*3!) = 105