The National Basketball Association (NBA) draftlottery

Chapter 4, Problem 4.15

(choose chapter or problem)

The National Basketball Association (NBA) draftlottery involves the 11 teams that had the worstwonlost records during the year. A total of 66balls are placed in an urn. Each of these balls isinscribed with the name of a team: Eleven havethe name of the team with the worst record, 10have the name of the team with the second-worstrecord, 9 have the name of the team with the thirdworstrecord, and so on (with 1 ball having thename of the team with the 11th-worst record).A ball is then chosen at random, and the teamwhose name is on the ball is given the first pickin the draft of players about to enter the league.Another ball is then chosen, and if it belongsto a team different from the one that received thefirst draft pick, then the team to which it belongsreceives the second draft pick. (If the ball belongs to the team receiving the first pick, then it is discardedand another one is chosen; this continuesuntil the ball of another team is chosen.) Finally,another ball is chosen, and the team named onthe ball (provided that it is different from theprevious two teams) receives the third draft pick.The remaining draft picks 4 through 11 are thenawarded to the 8 teams that did not win the lottery,in inverse order of their wonlost records.For instance, if the team with the worst record didnot receive any of the 3 lottery picks, then thatteam would receive the fourth draft pick. Let Xdenote the draft pick of the team with the worstrecord. Find the probability mass function of X.