Recall that a partition of a positive integer n means a way of writing n as the sum of some positive integers, where the order of the parts does not matter. For example, there are five partitions of 4:
4
3 + 1
2 + 2
2 + 1 + 1
1 + 1 + 1 + 1
How many partitions of 12 are there that have exacty least four parts?