In the sport of cricket, a team consists of 11 players who come up to bat in pairs. Initially,…

In the sport of cricket, a team consists of 11 players who come up to bat in pairs. Initially, players #1 and #2 bat. When one of those two players gets out, then player #3 replaces the one who got out. When one of the two batting players— player #3 and whichever player of {#1, #2} didn’t get out—gets out, then player #4 joins the one who isn’t out. This process continues until the 10th player gets out, leaving the last player not out (but stranded without a partner). Thus, in total, there are 11 players who bat together in 10 partnerships. As an example, consider the lineup Anil, Brendan, Curtly, Don, Eoin, Freddie, Glenn, Hansie, Inzamam, Jacques, Kumar. We could have the following batting partnerships: Anil & Brendan; Anil & Curtly; Anil & Don; Don & Eoin; Don & Freddie; . . . ; Don & Kumar.

1. How many different partnerships (pairs of players) are possible?

2. How many different sequences of partnerships (like the example list of partnerships given previously) are possible? (It doesn’t matter which of the last two players gets out.)



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