Explain two different methods for using combinations

[kerrwilk]

Homework Statement

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.

Homework Equations

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.

 

[Tedjn]

I am not certain to what the question is referring, but it could be the following: for every 45 students that travel by bus there are 5 students that travel by car. We can either choose the 45 bus students (method 1) or we can choose the 5 car students (method 2).