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I read the wikipedia article on combinations and saw two drawings there;_5_choose_3.svg;_5_multichoose_3.svg

and I am asking myself whats the points of them, does they make something easier to comprehend. Yes there is a pattern, but some pattern must arise, its not so that this pattern makes something easier. For me a textual description of how to generate all combinations is far more easier to understand. Or are these type of diagrams some special diagrams used in combinatorics?

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I think it's just different strokes for different folks. Some people find textual descriptions easier to understand, some, pictorial. If it doesn't work for you, ignore it and stick with what does work for you. – Gerry Myerson Nov 12 '12 at 0:27
For the left-hand pictures, spot that the top picture appears at the end of the bottom picture. – Henry Nov 12 '12 at 0:44

Personally I find the first easy to understand, both as a picture and as a list of numbers.

For the second, I find both sets of numbers easy to understand, and the pictures rather more thought-provoking, though next to the numbers they become clearer. The left-hand picture, once understood as stars and bars rather than just red and white, shows me that the number of possible multisets with $k$ elements drawn from $n$ distinct types is a combinatorial number ${n+k-1 \choose k}$.

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