A company has 5 applicants for 2 positions: 2 women and 3 men. The five applicants are equally qualified, and no preference is given to either gender. Let x be the number of women chosen to fill the 2 positions. What is p(x)?
There are two positions in the company and five applicants for the same, two women and 3 men. The probability p(x) has to be determined where x is the number of women chosen to fill the positions.
The total number of ways in which the positions can be filled is given by C(5, 2).
When x number of women fill the positions we have x number of women filling the positions in C(2, x) ways and 2-x women not filling the positions in C(3, 2-x) ways. This gives the number of ways in which x women can fill the positions as the product C(2, x)*C(3, 2-x)
The probability that the positions are filled by x women is C(2, x)*C(3, 2-x)/C(5, 2)
The value of x can be 0, 1 or 2.
The required value of p(x) = C(2, x)*C(3, 2-x)/C(5, 2)
http://www.math.hawaii.edu/~dale/373/07w.pdf see the 5th one.