If a committee of 3 is to be selected from a group of 15 students and 6 teachers, then the

Question

number of different possible committees that have at most 1 teacher is...

I got 1260 by doing (6C1)(15C1)(14C1), but the correct answer is supposed to be 1085. How did they get this?

Answer 1

At most 1 teacher ----> 1 teacher or no teacher

so C(6,1)*C(15,2) + C(6,0)*C(15,3)
= 6(105) + 1(455)
= 1085