Question #27b1c

1 Answer
Narad T.
Oct 26, 2016

The probability is =(26*51*2*46)/(25*33*49*97)=26⋅51⋅2⋅4625⋅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!))(nr)=n!(n−r!)(r!)

(""_4^100)= (100!)/((100-4!)(4!))=(100*99*98*97)/(1*2*3*4)=25*33*49*97(1004)=100!(100−4!)(4!)=100⋅99⋅98⋅971⋅2⋅3⋅4=25⋅33⋅49⋅97 ways

Choosing 2 Democrats from 52 is
(""_2^52)=(52!)/((50!)(2!))=(52*51)/(1*2)(522)=52!(50!)(2!)=52⋅511⋅2

Choosing 1 Independent from 2 is
(""_1^2)=(2!)/((1!)(1!))=(2*1)/(1*1)(21)=2!(1!)(1!)=2⋅11⋅1

Choosing 1 Republican from 46 is
(""_1^46)=(46!)/((45!)(1!))=(46)/(1*1)(461)=46!(45!)(1!)=461⋅1

So the probability is =(26*51*2*46)/(25*33*49*97)=26⋅51⋅2⋅4625⋅33⋅49⋅97

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