Question

Assume that a particular professional baseball team has 10 pitchers, 6 Infielders, and 9 other players. If 3 players' names are selected at random determine the probability that 2 are pitchers and 1 is an infielderWhat is the probability of selecting 2 pitchers and 1 infielder?Type an integer or a simplified fraction)

Answer 1

The probability of choosing 2 pitcher and one infielder out of the total number of player can be obtained as follows:

We need to slect two pitchers and one infielder out of 10 pitchers and 6 infielders, the number of ways we can do this is:

`(_(10)C_2)(_6C_1)=270`

Out of the 25 players if we choose 3 we can do this in the following number of possibilities:

`_(25)C_3=2300`

Then the probability is:

`P=(270)/(2300)=(27)/(230)`

Therefore, the probability of choosing 2 pitchers and one infielder is 27/230.