sananoor wrote:

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?

A) 50

(B) 55

(C) 75

(D) 100

(E) 250

Five juniors and five seniors (an equal number of juniors and seniors) should form 6-member team so that the team consists of at least four seniors (4, or 5 seniors, all 6 cannot be seniors since there are only 5 seniors).

1. 4 seniors and 2 juniors: \(C^4_5*C^2_5=5*10=50\)

2. 5 seniors and 1 juniors: \(C^5_5*C^1_5=1*5=5\)

Total = 50 + 5 = 55.

Answer: B.

Here is a Doubt.