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?

Exercise: counting committees 0.0/2.0 puntos (calificable) we start with a pool of n people. a chaired committee consists of k≥1 members, out of whom one member is designated as the chairperson. the expression k(nk) can be interpreted as the number of possible chaired committees with k members. this is because we have (nk) choices for the k members, and once the members are chosen, there are then k choices for the chairperson. thus, c=∑k=1nk(nk) is the total number of possible chaired committees of any size. find the value of c (as a function of n ) by thinking about a different way of forming a chaired committee: first choose the chairperson, then choose the other members of the committee. the answer is of the form c=(α+nβ)2γn+δ. what are the values of α , β , γ , and δ ?