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A committee of 5 will be chosen from a group of 4 men and 6 women....

A committee of 5 will be chosen from a group of 4 men and 6 women. What is the probability that at least 3 men are chosen?

Math   Statistics-And-Probability   
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Answer #1

Total number of people = (6+4) = 10

Number of men = 4

Number of women = 6

Number of members in committee = 5

number of ways of selecting 5 people out of 10 people = 10C5

number of ways of selecting 3 men out of 4 men = 4C3

number of ways of selecting 2 women out of 6 women = 6C2

number of ways of selecting 4 men out of 4 men = 4C4

number of ways of selecting 1 women out of 6 women = 6C1

P(atleast 3 men are chosen) = P(3 men , 2 women) + P(4 men + 1 women)

= ((4C3 6C2) + (4C4 6C1)) 10C5

= (60 + 6 ) 252

= 0.2619

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