Question

A City Council consists of nine men and six women. Three representatives are chosen at random to form a sub-committee. What is the probability one man and two women are chosen?

Answer 1

• 0.2967 or 29.67%

Explanation:

Total number of people

• 9 + 6 = 15

Combination of 3-people subcommitee without restrictions

• 15C3 = 15!/(15 - 3)!3! = 15!/12!3! = 15*14*13/2*3 = 455

Combination of 3-people subcommitee with one man ad two women

• 9C1*6C2 = 9*6!/(6-2)!2! = 9*6!/4!2! = 9*6*5/2 = 135

The probability of one man and two women are chosen

• P = 135/455 = 0.2967 or 29.67%