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 from the team's roster, determine the probability that all 3 are infielders.

Answer 1

Answer:
`(1)/(115)`

Explanation:

Given

there is 10 pitchers,6 infielders and 9 other players

3 players are selected at random

no of ways in which 3 infielders can be selected is
`^6C_3`

no of ways in which 3 players out of 25 players can be selected is

`^(25)C_3`

Therefore required probability is
`(^6C_3)/(^25C_3)=(1)/(115)`

Answer 2

there are 25 players on the team (10+6+9)

there are 6 infielders

They are picking without replacement

6/25 * 5/24 * 4/23

rearranging

6*4/24 *5/25 *1/23

1 *1/5 *1/23

1/115

Answer: 1/115