1. The problem statement, all variables and given/known data (A) Find and prove a bijection between the set of all functions from [n] to  and the set of all integers from 1 to 3n. (B) How many set partitions of [n] into two blocks are there? (C) How many set partitions of [n] into (n-1) blocks are there? (D) How many set partitions of [n] into (n-2) blocks are there? (E) How many ways can we split a group of 10 people into two groups of size 3 and one group of size 4? 2. Relevant equations 3. The attempt at a solution I'm not sure how to handle partitions of a set being mapped to another set. Could someone give me an idea of what definitions I would consider? I know (E) is done by equivalence relations and we could show two groups of size 3 are equal to each other, but I'm not sure how to use that. I'd like to know what method of attack I need to use to solve these problems, I'd assume it's similar for all of them?