# Question 27b1c

Oct 26, 2016

The probability is $= \frac{26 \cdot 51 \cdot 2 \cdot 46}{25 \cdot 33 \cdot 49 \cdot 97}$

#### Explanation:

We choose 4 among the 100 to calculate all the possible outcomes, it's a combination*
The formula used is
(""_r^n)= (n!)/((n-r!)(r!))

(""_4^100)= (100!)/((100-4!)(4!))=(100*99*98*97)/(1*2*3*4)=25*33*49*97 ways

Choosing 2 Democrats from 52 is
(""_2^52)=(52!)/((50!)(2!))=(52*51)/(1*2)

Choosing 1 Independent from 2 is
(""_1^2)=(2!)/((1!)(1!))=(2*1)/(1*1)

Choosing 1 Republican from 46 is
(""_1^46)=(46!)/((45!)(1!))=(46)/(1*1)#

So the probability is $= \frac{26 \cdot 51 \cdot 2 \cdot 46}{25 \cdot 33 \cdot 49 \cdot 97}$