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.

a.How many of the 210 subgroups of size six would contain exactly two women and four men? ( Hint: Compute the number of ways of selecting two out of the three women. Compute the number of ways of selecting four out of the seven men. Multiply the two results. That is, compute 3 C 2

times 7 C4 .) b. Compute the probability of randomly choosing a sample of six applicants that contains exactly two women and four men. ( Hint: Use the classical "Favorable over Total " approach to probability. Divide your answer to part a by the total number of samples of size 6 that could be selected210 in this case.)