$4\mathrm{.}15.$ The National Basketball Association $($NBA$)$ draft lottery involves the $11$ teams that had the worst won$-$lost records during the year. A total of $66$ balls are placed in an urn. Each of these balls is inscribed with the name of a team: Eleven have the name of the team with the worst record, $10$ have the name of the team with the second$-$worst record, $9$ have the name of the team with the third$-$worst record, and so on $($with $1$ ball having the name of the team with the $11$th$-$worst record$).$ A ball is then chosen at random, and the team whose name is on the ball ispick, then the team to which it belongs receives the second draft pick. $($If the ball belongs to the team receiving the first pick, then it is discarded and another one is chosen; this continues until the ball of another team is chosen.$)$ Finally, another ball is chosen, and the team named on the ball $($provided that it is different from the previous two teams$)$ receives the third draft pick. The remaining draft picks $4$ through $11$ are then awarded to the $8$ teams that did not "win the lottery," in inverse order of their won$-$lost records. For instance, if the team with the worst record did not receive any of the $3$ lottery picks, then that team would receive the fifth drafts pick. Let X denote the draft pick or the team with the worst record. Find the PMF of X