The sales force of a business consists of 10 men and 10 women. A production unit of 6 people is set up at random. What is the probability that it will consist of 2 men and 4 women? (type answer as an integer or decimal rounded to four decimal places as needed) How is this done?

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# 2 Answers

You're first picking 6 people out of 20 possible candidates, so the total number of possible 6-person combinations is
_{20}C_{6}. By the same logic, the number of possible male combinations are
_{10}C_{2} and the female combinations _{10}C_{4}; these two are independent events, so the number of possible 2-man and 4-woman combinations are (_{10}C_{2})(_{10}C_{4}).

The possibility of this happening, then, is (_{10}C_{2})(_{10}C_{4})/_{20}C_{6}.

Picking 2 men out of 10 men: C(10, 2);

Picking 4 women out of 10 women: C(10, 4);

Picking 6 persons out of 20 persons: C(20, 6)

Probability

= #favorable outcomes/#total outcomes

= [C(10, 2) * C(10, 4)]/C(20, 6), multiplication principle for independent events

= 315/1292

= .2438 <==Answer