Question 1122883
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.