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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?

Sagot :

Mhanifaidn

Answer:

  • 0.2967 or 29.67%

Step-by-step 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%
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