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Stars and Bars

Distributing identical objects into distinct bins, via a bijection to arrangements of stars and dividing bars.

Discrete Mathematics: An Open Introduction, Stars and Bars

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1 exercise

Exercise 3

Each of the counting problems below can be solved with stars and bars. For each, say what outcome the diagram represents, if there are the correct number of stars and bars for the problem. Otherwise, say why the diagram does not represent any outcome, and what a correct diagram would look like.

  1. How many ways are there to select a handful of 6 jellybeans from a jar that contains 5 different flavors…

2.5
Combinatorial ProofsAdvanced Counting Using PIE

Adapted from Discrete Mathematics: An Open Introduction © 2013–2019 Oscar Levin. Licensed under CC BY-SA 4.0. Source: Discrete Mathematics: An Open Introduction. Imported at revision 1e2e26b.

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