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Assume that a particular professional baseball team has 10 pitchers, 7 infielders, and 8 other players. If 3 players' names are selected at random, what is the probability of selecting 2 pitchers and 1 infielder?

User Bluemind
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1 Answer

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Final answer:

To find the probability of selecting 2 pitchers and 1 infielder, we need to determine the total number of possible combinations and the number of combinations with 2 pitchers and 1 infielder. The probability is calculated as the ratio of the number of desired combinations to the total number of combinations.

Step-by-step explanation:

To find the probability of selecting 2 pitchers and 1 infielder, we need to determine the total number of possible combinations of 3 players and the number of combinations that have 2 pitchers and 1 infielder.

The total number of players is 10 pitchers + 7 infielders + 8 other players = 25. Therefore, there are 25 choose 3 = C(25, 3) possible combinations of 3 players.

To calculate the number of combinations with 2 pitchers and 1 infielder, we need to choose 2 out of the 10 pitchers and 1 out of the 7 infielders. This can be done using the combination formula: C(10, 2) * C(7, 1).

The probability of selecting 2 pitchers and 1 infielder is the ratio of the number of combinations with 2 pitchers and 1 infielder to the total number of combinations. Therefore, the probability is: (C(10, 2) * C(7, 1)) / C(25, 3).

User Rene Just Nielsen
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