How many different committees can be formed from 5 professors, and 15 students. If each committee is made up of 2 professors, and 10 students.

Answer 1

5 choose 2 * 15 choose 12
=5C2*15C12
=5!/(2!3!) * 15!/(12!3!)
=5*4/2! * 15*14*13/6
=10*455
=4550