can you explain this problem?

Question

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?

Answer 1

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.

Answer 2

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