In Demonstration Exercise 4.16, we determined that there are 210 different subgroups of size six that could be produced from the pool of ten applicants. Suppose the applicant pool is made up of three women and seven men.

In Exercise 16
The price of Albertson stock increased on 40% of the trading days over the past year. The price of Boeing stock increased on 30% of the trading days. On 60% of the days that the price of Albertson stock increased, the price of Boeing stock increased as well.

a. How many of the 210 subgroups of size six would contain exactly two women and four men?

b. Compute the probability of randomly choosing a sample of six applicants that contains exactly two women and four men.