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Counting Partitions and Bijections

  1. Sep 26, 2011 #1
    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?
     
  2. jcsd
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