Answer:
P=0.228
Step-by-step explanation:
We know that from a faculty of six professors, six associate professors, ten assistant professors, and twelve instructors, a committee of size six is to be selected.
Therefore, we have 34 people.
We calculate the number of possible combinations:
[tex]C^{34}_6=\frac{34!}{6!(34-6)!}=1344904\\[/tex]
Of the 6 professors we choose 2, and of the other 28 people we choose 4.
We calculate the number of favorable combinations:
[tex]C_2^6\cdot C_4^{28}=\frac{6!}{2!(6-2)!}\cdot \frac{28!}{4!(28-4)!}=15\cdot 20475=307125\\[/tex]
Therefore, the probability is:
[tex]P=\frac{307125}{1344904}=0.228[/tex]
