Question

The math department of a college has 20 faculty members, of whom 5 are women and 15 are men. A curriculum committee of 4 faculty members is to be selected. A. How many ways are there to select the committee that has more women than men?B. How many ways are there to select a committee?
C. If the positions in the committee are titled chair, vice chair, and secretary, in how many ways can this committee be formed among the 24 AMS faculty members?

Answer 1

Answer:

a) Therefore, exists 155 ways.

b) Therefore, exists 4845 ways.

c) That is not possible.

Step-by-step explanation:

We know that the math department of a college has 20 faculty members, of whom 5 are women and 15 are men. A curriculum committee of 4 faculty members is to be selected.

a) We calculate how many ways are there to select the committee that has more women than men

$C^5_4\cdot C^{15}_0+C^5_3\cdot C_1^{15}=5\cdot 1+ \frac{5!}{3!(5-3)!}\cdot 15=5+150=155$

Therefore, exists 155 ways.

b) We get:

$C_4^{20}=\frac{20!}{4!(20-4)!}=4845$

Therefore, exists 4845 ways.

c) That is not possible.