Mathematics: Combinations and Counting

Question

You are managing a staff of 20 engineers and 40 technicians. For an upcoming project, you must select 2 engineers and 5 technicians. How many different teams are possible?

Answer 1

(20 choose 2)(40 choose 5) <-- order is not important

(20*19/2) ( 40*39*38*37*36/(5*4*3*2*1)) =

190* ( 13*38*37*36) <--- 2 cancels 20; 5*4*2 cancels 40; 3 cancels 39