Question

4. From a faculty of six professors, six associate professors, ten assistant professors, and twelve instructors, a committee of size six is to be selected. What is the probability that the number of selections include exactly two professors?

Answer 1

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:

$C^{34}_6=\frac{34!}{6!(34-6)!}=1344904$

Of the 6 professors we choose 2, and of the other 28 people we choose 4.

We calculate the number of favorable combinations:

$C_2^6\cdot C_4^{28}=\frac{6!}{2!(6-2)!}\cdot \frac{28!}{4!(28-4)!}=15\cdot 20475=307125$

Therefore, the probability is:

$P=\frac{307125}{1344904}=0.228$