if there are fifteen football games, with an outcome of win or lose, how many different possible combinations are there

Question

 If there are 15 football matches, with an outcome of win or lose, how many different possible outcomes are there?

Answer 1

I take it that two outcomes are equivalent if the team wins the same number of games in each series. In this case the only number that matters is the number W of wins in the series. This number can only take the values 0, 1, 2, ... , 15, and each of these is different. Therefore there are 16 possible outcomes.

 

If the order of wins and losses matters, then there are 2¹⁵ possible outcomes, as each game has two possibilities and there are 15 of them.