How many soccer teams (11 players) can be formed from combinations of various numbers of goal keepers, fullbacks, halfbacks, and forwards?


Enter the numbers of players on a team that specialize in the following positions as represented by:

A soccer team has 1 goal keeper (goalie), 2 fullbacks, 3 halfbacks, and 5 forwards. How many 11-person teams can be composed from the above box entries for the number of team members specializing in one of the 4 positions? This is found by taking the combinations of the number of goalies taken 1 at a time, the combinations of the number of fullbacks taken 2 at a time, the combinations of the number of halfbacks taken 3 at a time, and the combinations of the number of forwards taken 5 at a time, and multiplying these combination numbers. For example, if a team has 2 goalies, 4 fullbacks, 6 halfbacks, and 8 forwards, then 2C1*4C2*6C3*8C5 (where 8C5 stands for the combinations of 8 things taken 5 at a time etc.) is the number of different teams that can be formed. This would be 2!/(1!1!) * 4!/(2!2!) * 6!/(3!3!) * 8!/(3!5!) = 13440 teams.
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