How many ways can you find whole numbers adding up to five if the order matters? [So 1 + 4 and 4 + 1 count as two different ways or 3+ 1 + 1 and 1 + 3 + 1]. Even though there's no actual addition involved we'll count 5 by itself as 1 way. This is a bit of a weird thing to do but mathematicians do this sometimes and it will make more sense later.
Technical point: actually 0 is a whole number so I should have said whole numbers greater than 0 (that is: 1, 2, 3, etc). These are called the Natural numbers.
Partitions of (5) = 7 [This is called the "Partition Function"]
5 = 5
4 + 1 = 5
3 + 2 = 5
3 + 1 + 1 = 5
2 + 2 + 1 = 5
2 + 1 + 1 + 1 = 5
1 + 1 + 1 + 1 + 1 = 5
You can put them in any order you want, such as: 1+1+3, 1+3+1, 3+1+1.....etc., and then count them.
