To perform during the improvisation section of their concert, the director of the school of jazz band draws lots to randomly choose 4 players from the 4 trumpet players, 5 saxophone players, and 2 keyboard players. What is the probability the director picks no keyboard players?

Answer 1

First, let's calculate the total number of ways the director can choose 4 players from the 11 total players:

11 players choose 4 = 11! / (4! * 7!) = 330 ways

Next, let's calculate the number of ways the director can choose 4 players without picking any keyboard players. This means the director must choose all players from the 9 trumpet and saxophone players:

9 players choose 4 = 9! / (4! * 5!) = 126 ways

Therefore, the probability of the director picking no keyboard players is:

Number of favorable outcomes / Total number of outcomes = 126 / 330 ≈ 0.38

So, the probability the director picks no keyboard players is approximately 0.38 or 38%.