Question

A college basket ball team has 15 players, 5 seniors, 8 juniors, and 2 sophomores. Two players are randomly selected to serve as captain for the next game, what’s he probability both selected are seniors?

Answer 1

Answer
We have a total of 15 players, which consists of 5 seniors, 8 juniors and 2 sophomores
We need to the find the probability of selecting both captains from seniors.
Number of ways of selecting both captain from senior is C(5,2)*C(8,0)*C(2,0)
C stands for combination
We know that Combination(8,0) = 8!//[(8-0)!*0!] = 1
And Combination(2,0) = 2!//[(2-0)!*0!] = 1
So, Number of ways of selecting both captain from senior is C(5,2)*C(8,0)*C(2,0), this can be written as
Number of ways of selecting both captain from senior = C(5,2)*1*1 = 5!/[(5-2)!*2!] = 10 ways
Number of ways of selecting 2 players from 15 = Combination(15,2) = 15!/[(15-2)!*2!] = 105

So, the required probability = C(5,2)/ C(15,2) = 10/105 = 0.0952 (rounded to 4 decimal places)