Question

4 players are to be picked from a group of 11 seniors, 8 juniors, and 5 freshmen at random. What is the probability that at least 2 freshmen are selected?

Answer 1

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

Number of freshmen = 5

Number of non-freshmen = 11 + 8 = 19

Total number of students = 11 + 8 + 5 = 24

Number of ways to select 4 students from 24 = 24C4

= 10,626

P(at least 2 freshmen are selected) = Number of ways to select at least 2 freshmen / Number of ways to select 4 students from 24

= (Number of ways to select 2 freshmen and 2 non-freshmen + Number of ways to select 3 freshmen and 1 non-freshmen + Number of ways to select 4 freshmen)/Number of ways to select 4 students from 24

= (5C2 x 19C2 + 5C3 x 19 + 5C4)/10,626

= (10 x 171 + 10 x 19 + 5)/10,626

= 0.1793