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

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

Answer 2

Answer:$\frac{1}{115}$

Step-by-step 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 $\frac{^6C_3}{^25C_3}=\frac{1}{115}$