Combinations of partitions--504 students problem?

his is a very interesting problem using Partitioning of Integers. Here we have 504 gifts and 4 categories for which they can be given. If we keep all 504 in a row we need say 3 sticks to make 4 partitions of it. for example one such would be 200 | 100 | 100 | 104 and so on So basically we have 507 spots and we are choosing such that 3 of them are sticks. So number of combinations become 507 C 3 = 21592285.