Question

In a church wing with 8 men and 10 women members find the probability that a 5 member committee chosen randomly will have.......

a).all men.
b).3men and 2 women​

Answer 1

a) Probability that a 5 member committee will have all men = 0.0065

b) probability that a 5 member committee chosen randomly will have 3 men and 2 women = 0.294

Explanation:

Number of men = 8

Number of women = 10

Total number of members = 10 + 8 = 18

Probability = (Number of possible outcomes)/(Total number of outcomes)

Number of ways of selecting a 5 member committee from 18 people =
`^(18)C_5 = (18!)/((18-5)!5!) = (18!)/(13!5!)` = 8568 ways

a) Probability that a 5 member committee will have all men

Number of ways of selecting 5 men from 8 men

=
`^8C_5 = (8!)/((8-5)!5!) = (8!)/(3!5!)` = 56 ways

Probability that a 5 member committee will have all men = 56/8568

Probability that a 5 member committee will have all men = 0.0065

b)probability that a 5 member committee chosen randomly will have 3men and 2 women​

Number of ways of selecting 3 men from 8 men

=
`^8C_3 = (8!)/((8-3)!3!) = (8!)/(5!3!)` = 56 ways

Number of ways of selecting 2 women from 10 men

=
`^(10)C_2 = (10!)/((10-2)!2!) = (10!)/(8!2!)` = 45 ways

Number of ways of selecting 3 men and 2 women = 56*45

Number of ways of selecting 3 men and 2 women = 2520

Probability of selecting 3 men and 2 women = 2520/8568 = 0.294

probability that a 5 member committee chosen randomly will have 3 men and 2 women = 0.294