In: Statistics and Probability
Given
Total number of people = 12
Number of Democrats = 6
Number of Republicans = 4
Number of Independents = 2
Number of people to be chosen = 5
A)
The possible number of committes
= 792 ways
B)
The possible number of committes consist of 2 Democrats, 2 Republicans, and 1 Independent
= 180 ways
C)
From above,
The possible number of committes chosen ( chosen 5 people from a collection of 12 people)= 792 ways
The possible number of committes consist of 2 Democrats, 2 Republicans, and 1 Independent = 180 ways
Now,
the probability that the committee consists of 2 Democrats, 2 Republicans, and 1 Independent = 180 / 792 = 0.2273
D)
Possible Committee:
i) 4 Democrats, 1 Republicans
ii) 4 Democrats, 1 Independent
iii) 5 Democrats
Now,
The possible number of committees that consist of at least 4 Democrats
= 96 ways