A starting lineup in basketball consists of 2 guards, 2 forwards, and 1 center. (a) A certain college team has on its roster 5 guards, 4 forwards, 3 centers. How many
different starting lineups can be created?
(b) Suppose that Mary is listed on the roster as a forward, and Alice is listed on the
roaster as a center. Assume that, for a given starting lineup, all players are randomly
chosen for each role among qualified players on the roster (guards are chose among
guards only, etc.). What is the probability that Mary and Alice will get on the
lineup?