SOLUTION: In how many ways can the coaches of a basketball team select a most valuable player, a most improved player, and a best defensive player from the 12 player on a team?

Question 275593: In how many ways can the coaches of a basketball team select a most valuable player, a most improved player, and a best defensive player from the 12 player on a team?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

That depends. I don't see any reason why the MVP, most improved, and best defensive player cannot all be the same person, unless the coaches have placed some sort of arbitrary restriction on the selection process that says the awards have to go to three different people.

Without the "three different people" rule:

Twelve ways to choose the MVP. For each of those twelve, twelve ways to choose the MIP. For each of those 144 ways, 12 ways to choose the best defensive player, so:

With the "three different people" rule:

12 ways to pick MVP times 11 ways to pick MIP times 10 ways to pick best defense.

John

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