Need help understanding book description for a combinatoris problem

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SUMMARY

The discussion centers on a combinatorics problem regarding the number of ways to express the number 4 as the sum of 5 non-negative integers. The user grapples with understanding the solution provided in their textbook, specifically regarding the potential for repeated combinations leading to the same sum. The confusion arises from the interpretation of selections of integers corresponding to "boxes" and how these selections can yield identical results despite differing combinations. The user acknowledges the need to relocate the inquiry to a more appropriate section for textbook problems.

PREREQUISITES
  • Understanding of basic combinatorics principles
  • Familiarity with non-negative integer partitions
  • Knowledge of generating functions in combinatorics
  • Ability to interpret mathematical problem statements
NEXT STEPS
  • Study the concept of "stars and bars" in combinatorics
  • Explore non-negative integer solutions to equations
  • Learn about generating functions for counting partitions
  • Review examples of combinatorial proofs to solidify understanding
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Students of mathematics, particularly those studying combinatorics, educators seeking to clarify concepts, and anyone interested in solving partition problems involving non-negative integers.

fleazo
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*combinatorics*, sorry for the typo in the title. The problem is as follows: In how many ways can we write the number 4 as the sum of 5 non-negative integers?

I have taken a screen cap of the solution that my book provides. Here it is

http://imgur.com/8BhxXPq

So I understand the concept of how they're explaining this - for example - one possible selection is I chose "box 1" 2 times, "box 2" 1 time, "box 3" 0 times, "box 4" 2 times, and "box 5" 0 times, this corresponds to : 2 + 1 + 2 = 5.

The confusion for me is, it seems like this approach would have a lot of repeats. For example - the selection of "box 1" 0 times, "box 2" 0 times, "box 3" 2 times, "box 4" 1 time, and "box 5" 2 times, would also produce : 2 + 1 + 2 = 5.I realize I'm missing something in the logic, but I'm not sure what.
 
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oops... I realize now this is a textbook problem and not allowed here. I'm moving it to the textbook problem section. Sorry about that.
 

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