Let's say I have 12 different Baseball games. There is one of only 2 possible outcomes for each of the 12 games. How would I fugure out how many combinations there are for the 12 games and for 11,10, and so fourth.
Thank
you.
Fabian
Hi Fabian,
I t hink about keeping a record book, a record of the outcomes of the games. I will distinguish the outcomes by recording the result for the home team, either win (W) or lose(L). Each game will be a column in my record book.
For one game I need one column and two rows.
| Game 1 |
|---|
| W |
| L |
For two games I need two columns and 2 
2
= 4 rows.
| Game 1 | Game 2 |
|---|---|
| W | W |
| W | L |
| L | W |
| L | L |
I had to double the number of rows since each row in the previous record book gets extended to two possible outcomes for the next game.
For three games I need three columns and 2 4
= 8 rows.
| Game 1 | Game 2 | Game 3 |
|---|---|---|
| W | W | W |
| W | W | L |
| W | L | W |
| W | L | L |
| L | W | W |
| L | W | L |
| L | L | W |
| L | L | L |
Again I had to double the number of rows since each row in the previous record book gets extended to two possible outcomes for the next game.
How many rows do you need for four games?
Penny