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) <pre><font size = 4 color = "indigo"><b>Exactly</pre></font></b>one has a college degree<pre><font size = 4 color = "indigo"><b>

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*6C2=10*15=150}}}

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

So the desired probability is {{{150/560=15/56}}}

</pre></font></b>
ii) at least 2 have a college degree
<pre><font size = 4 color = "indigo"><b>

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*6C1=45*6=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 {{{390/560=39/56}}}

Edwin</pre>