combination question

Question

An equal number of juniors and seniors are trying out for six spots on the university debating team. If the team must consist of at least four seniors, then how many different possible debating teams can result if five juniors try out?


The answer is 55.

Why?

Answer 1

4 seniors/2 juniors is 5C4 (5C2) different ways of getting 6 on debate team

5 seniors/1 junior   is 5C5 (5C1) different ways of getting 5 seniors on debate team

 

The first computation is 5(10) = 50 & the second computation is 1(5) = 5 so that is indeed total of 55 ways.