Crestwood Elementary School has an active four-square league, consisting of ten players, including Justin and Tim. Each day at recess, the ten players split into two four-square games, each with five players in no relevant order. Over the course of a semester, each possible match-up of five players occurs once. How many times did Justin play in the same game as Tim?
+130517 Consider that Justin and Tim comprise two of the players in a five player set where the other players are "A," "B" and "C"
Then, each possible set looks like this:
{A, B, C, Justin, Tim }
Then, we just want to choose any 3 of the 8 remaining players to comprise all these possible sets
So C(8,3) = 56
So....they played on the same team 56 times
+130517 Consider that Justin and Tim comprise two of the players in a five player set where the other players are "A," "B" and "C"
Then, each possible set looks like this:
{A, B, C, Justin, Tim }
Then, we just want to choose any 3 of the 8 remaining players to comprise all these possible sets
So C(8,3) = 56
So....they played on the same team 56 times
