How many basketball teams can be formed from combinations of guards, centers, and forwards?


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

A basketball team has 2 guards, 2 forwards, and one center. How many 5-man teams can be composed from the above box entries for the number of team members specializing in one of the three positions? This is found by taking the combinations of the number of guards taken 2 at a time, the number of forwards taken 2 at a time, and the number of centers taken one at a time, and multiplying the numbers. For example, if a team has 6 guards, 2 centers, and 5 forwards, then 6C2*2C1*5C2 (where 6C2 stands for the combinations of 6 things taken 2 at a time etc.) is the number of different teams that can be formed. This would be 6!/(4!2!)* 2!/(1!1!) * 5!/(3!2!) = 300 teams.
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