SOLUTION: 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) one has a college dgr

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Question 296311: 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) one has a college dgree
ii) at least 2 have college dgree
thank you

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
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 = 10C1%2A6C2=10%2A15=150

The denominator is "16 choose 3" or 16C3 or 560.

So the desired probability is 150%2F560=15%2F56


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"

10C2%2A6C1=45%2A6=270 

plus 

2.  the number of ways exactly 3 (all 3) have college degrees (and none don't), which is "10 choose 3", or

10C3+=+120   

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 390%2F560=39%2F56

Edwin