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?
can you explain this problem?
You're first picking 6 people out of 20 possible candidates, so the total number of possible 6-person combinations is 20C6. By the same logic, the number of possible male combinations are 10C2 and the female combinations 10C4; these two are independent events, so the number of possible 2-man and 4-woman combinations are (10C2)(10C4).
The possibility of this happening, then, is (10C2)(10C4)/20C6.
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)
= #favorable outcomes/#total outcomes
= [C(10, 2) * C(10, 4)]/C(20, 6), multiplication principle for independent events
= .2438 <==Answer