Suppose that 27 students get together to play soccer. (a) There are three different fields for…

Suppose that 27 students get together to play soccer.

(a) There are three different fields for the students to practice on. How many different ways are there to assign the 27 players to the 3 fields in teams of 9?

(b) How many ways are there to assign the 27 players to 3 teams of 9, without regard for which team is on which field?

(c) How many ways are there to assign the 27 players to 3 teams of 9, and −1 for each team to choose 1 of its players as captain?

(d) One of the teams plays 10 games against teams from other schools, ending the season with a 7-3 record. How many different sequences of wins and losses could have led to this outcome?

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