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](https://tex.z-dn.net/?f=C%5E5_4%5Ccdot%20C%5E%7B15%7D_0%2BC%5E5_3%5Ccdot%20C_1%5E%7B15%7D%3D5%5Ccdot%201%2B%20%5Cfrac%7B5%21%7D%7B3%21%285-3%29%21%7D%5Ccdot%2015%3D5%2B150%3D155)
Therefore, exists 155 ways.
b) We get:
![C_4^{20}=\frac{20!}{4!(20-4)!}=4845](https://tex.z-dn.net/?f=C_4%5E%7B20%7D%3D%5Cfrac%7B20%21%7D%7B4%21%2820-4%29%21%7D%3D4845)
Therefore, exists 4845 ways.
c) That is not possible.
Answer:
<h2>9(2n + 1) = 18n + 9</h2>
Step-by-step explanation:
9(2n + 1)
<em>use the distributive property a(b + c) = ab + ac</em>
= (9)(2n) + (9)(1) = 18n + 9
Answer:
A+B+C=180°( BY SUM OF ALL ANGLE IS 180°)
70°+40°+C=180°
110°+C=180°
C=180°-110°
C=70°
C+X=180°(BY LINEAR PAIR)
70°+X=180°
X=180°-110°
X=70°