Question 1122883: From a faculty of six professors, six associate professors, ten assistant professors,
and twelve instructors, a committee of size six is formed randomly. What is the
probability that (a) there are exactly two professors on the committee; (b) all
committee members are of the same rank?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 34 total people, number of ways to choose six is 34C6=1344904
exactly two professors is 6C2, and ways to choose the rest are 28C4. That product is 15*20475=307125, so probability overall is 0.2284
There is 1 way to choose 6 professors for the committee (all of them), 1 more way for all associate professors
10C6 for the assistant professors (210) and 12C6 for the instructors, or 924. Each of these is added for 1136 possibilities or probability 0.0008.
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