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

P=0.228

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=(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)=(6!)/(2!(6-2)!)\cdot (28!)/(4!(28-4)!)=15\cdot 20475=307125\\`

Therefore, the probability is:

`P=(307125)/(1344904)=0.228`