How many possibilities is there for 15 games of win and loses

Question

If you have 15 football games how many different combinations would I have to pick in order to cover ever possible win loss scenario

Answer 1

Problems like this are easier if you break them into smaller parts. A game only has two possibilities, win or loose. If we create a tree of possible seasons maybe we will find a pattern.

Game 1: W L

Game 2: W L W L

Game 3: W L W L W L W L

We could continue this all the way to game 15. Each path you take down this tree will represent a unique season. Start at the top, taking a right represents a loss going to the left represents a win. The number of letters in each row represents the number of possible seasons after that many games, after 1 game its 2. After two games its 4. After three games its 8. Do you see the pattern? The number of possible seasons is 2^(number of games). A 15 game season would be 2^(15), or 32,768 possible seasons.