Bunuel 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

Kudos for correct solution.

Here it is given as five juniors try out i.e we have 5 juniors and 5 seniors since equal number try out for the six spots

Now we can have two combination

first one - 4 seniors and 2 juniors = 5C4 * 5C2 =50 (We have to keep minimum nos of seniors to 4 as the statement says atleast 4 numbers of seniors are in the team)

Second one- 5 seniors and 1 juniors = 5C5 * 5C1 = 5

Therefore total possible teams = 50 + 5 =55

_________________

If you found this post useful, please let me know by pressing the Kudos Button