Among a 16 applicants for a job, 10 have college dgrees. If three of the applicants are randomly selected for interviews, what are the probabilites that :
i) Exactly
one has a college degree
The numerator is the number of ways to chose 1 college grad and 2
non-grads. That's "10 choose 1" times "6 choose 2", or
Numerator of desired probability =
The denominator is "16 choose 3" or 16C3 or 560.
So the desired probability is
ii) at least 2 have a college degree
The number of possibilities here is the sum:
1. the number of ways exactly 2 have college degrees (and 1 doesn't),
which is "10 choose 2" times "6 choose 1"
plus
2. the number of ways exactly 3 (all 3) have college degrees (and none don't), which is "10 choose 3", or
So the numerator of the desired probability is this total: 270+120=390
The denominator is, as before in part i), "16 choose 3" or 16C3 or 560.
So the desired probability is
Edwin