A soccer coach organizing a field trip finds that 50 students have signed up. However, the bus has only 47 seats, so a few students will have to travel by car. The coach and one other coach must go on the bus. Explain two different methods for using combinations to find how each coach can choose which students go on the bus. Show that both methods produce the same answer.
The Attempt at a Solution
I determined that the number of combinations of students on the bus is 50 C 45 = 2118760. However, I do not know how this can be done with two different methods. Could someone please help me? Thanks.