Question

Assume that a particular professional baseball team has 11 pitchers, 5 infielders, and 13 other players. If 3 players' names are selected at random, what is the probability that all 3 are infielders?

Answer 1

To find the probability that all 3 players are infielders, we need to use the combination formula. The probability is given by the number of ways to choose 3 infielders out of 5 divided by the number of ways to choose 3 players out of the total number of players.

Step-by-step explanation:

To find the probability that all 3 players are infielders, we need to first determine the total number of possible outcomes and the number of favorable outcomes. The total number of players is 11 pitchers + 5 infielders + 13 other players = 29.

Since we are selecting 3 players at random, the total number of possible outcomes is the number of ways we can choose 3 players out of 29, which is given by the combination formula C(29, 3). The number of favorable outcomes is the number of ways we can choose 3 infielders out of the 5, which is given by the combination formula C(5, 3).

Therefore, the probability that all 3 players are infielders is:

P(all 3 are infielders) = C(5, 3)/C(29, 3)