Question

Question #27b1c

Answer 1

The probability is `=(26*51*2*46)/(25*33*49*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 `=(26*51*2*46)/(25*33*49*97)`