# Counting Partitions and Bijections

1. Sep 26, 2011

### Curiouspoet

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 [3] 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?