SOLUTION: The Red Cross honors and recognizes its best volunteers from time to time. One of the Red Cross offices has received 12 nominations for the next group of 4 volunteers to be rec

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Question 1177246: The Red Cross honors and recognizes its best volunteers from time to time.
One of the Red Cross offices has received 12 nominations for the next group
of 4 volunteers to be recognized. Eight of these 12 nominated volunteers are
females. If the Red Cross office decides to randomly select 4 names out of
these 12 nominated volunteers, find the probability that of these 4
volunteers
a. exactly 3 are females
b. exactly 1 is female
c. at most 1 is female

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
12 people: 8F and 4M
select 4 names:  12C4 all the ways this can be done.

P(exactly 3 are females) =  (8C3)(4C1)/(12C4)

P(exactly 1 is female) = (8C1)(4C3)/(12C4)

P(at most 1 is female) = 1- P(no females) = 1 - (4C4)/(12C4)

Wish You the Best in your Studies.