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I read the wikipedia article on combinations and saw two drawings there

http://en.wikipedia.org/wiki/File:Combinations_without_repetition;_5_choose_3.svg

http://en.wikipedia.org/wiki/File:Combinations_with_repetition;_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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    For the left-hand pictures, spot that the top picture appears at the end of the bottom picture.2012-11-12

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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 ${n+k-1 \choose k}$.