From a group of three data processing managers, two senior systems analysts, and two quality control engineers, three people are to be randomly selected to form a committee that will study the feasibility of adding a dual-core CPU cooler at a consulting firm. Let X denote the number of data-processing managers and Y the number of senior systems analysts selected for the committee.
a. Find the joint probability distribution of X and Y.
b. Find the marginal distribution of X.