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
[tex]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[/tex]
Therefore, exists 155 ways.
b) We get:
[tex]C_4^{20}=\frac{20!}{4!(20-4)!}=4845[/tex]
Therefore, exists 4845 ways.
c) That is not possible.
