# File:Combinations with repetition; 5 multichoose 3.svg

Original file(SVG file, nominally 626 × 685 pixels, file size: 701 KB)

 Description There's a bijection between the k-element multisets with elements from an n-element set    (k-combinations of n elements with repetitions) and the k-element subsets of an n+k−1-element set    (k-combinations of n+k−1 elements without repetitions). ${\displaystyle \left(\!\!{n \choose k}\!\!\right)={\binom {n+k-1}{k}}}$ This file shows the bijection between the 3-element multisets with elements from ${\displaystyle \{1,2,3,4,5\}}$    (right side) and the 3-element subsets of a 7-element set    (left side). ${\displaystyle \left(\!\!{5 \choose 3}\!\!\right)={\binom {5+3-1}{3}}={\binom {7}{3}}=35}$ The first line represents the following correspondence between a 7-tuple, a 5-tuple and a 3-element multiset: (1,1,1,0,0,0,0) ≙ (3,0,0,0,0) ≙ {1,1,1} The scetches between 7- and 5-tuples are meant to be intuitive, and do not represent mathematical objects. Date 2011 Source Own work Author Watchduck (a.k.a. Tilman Piesk) Other versions Printable version: File:Combinations with repetition; 5 multichoose 3.pdf

## Related files

without repetition with repetition
Variations

${\displaystyle ~{5 \choose 3}{\cdot 3!}~=~60~}$

${\displaystyle ~5^{3}~=~125~}$

Combinations

${\displaystyle ~{5 \choose 3}~=~10~}$

${\displaystyle ~\left(\!\!{5 \choose 3}\!\!\right)~=~{7 \choose 3}~=~35~}$

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Date/TimeThumbnailDimensionsUserComment
current18:49, 26 April 2011626 × 685 (701 KB)Watchducktext into objects
17:45, 26 April 2011626 × 685 (738 KB)Watchduck{{Information |Description= |Source={{own}} |Date=2011 |Author= Lipedia |Permission= |other_versions= }} == Licensing: == {{self|GFDL|cc-by-3.0}} Category:Combinatorics
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