a committee of three is to be chosen from a group consisting of 5 men and 5 women. if the selection is made at random, find the probability that (a) all three men , (b) two are men.
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Step-by-step explanation:
Total number of persons = 10.
Number of persons to be selected = 3.
Total number of ways = C(10,3)
= 120.
Now,
Total number of men = 5
Total number of women = 5.
(i) All three men:
Number of ways to select 3 men = C(5,3) = 10.
P(All three men are selected) = (10/120)
= 1/12
(ii) Two are men:
Number of ways to select 2 men = C(5,2) = 10.
Number of ways to select 1 women = C(5,1) = 5
P(Two are men) = (10 * 5)/120
= 50/120
= 5/12.
Hope it helps!
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