There are 30 teams in the National Basketball Association: 15 in the West- ern Conference, and 15 in the Eastern Conference. (a)
Suppose each of the teams in the league has one pick in the first round of the NBA draft. How many ways are there to arrange the order of the teams selecting in the draft? (b) Suppose that each of the first three positions in the draft must be awarded to one of the fourteen teams that did not advance to the play- offs that year. How many ways are there to assign the first three posi- tions in the draft? (c) How many ways are there for eight teams from each conference to advance to the playoffs, if order is unimportant? (d) Suppose that every team has three centers, four guards, and five for- wards. How many ways are there to select an all-star team with the same composition from the Western Conference?
