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Ball Picking


Consider an infinite repository containing balls of n different types. Then the following table summarizes the number of distinct ways in which k balls can be picked for four common definitions of "distinct."

type of pickingnamesymbol namesymbol
ordered samples with replacementstringpowern^k
ordered sample without replacementpermutation_nP_k=(n!)/((n-k)!)
unordered samples with replacementmultisetmultichoose((n; k))=(n+k-1; k)
unordered samples without replacementcombinationbinomial coefficient, choose_nC_k=(n; k)=(n!)/(k!(n-k)!)

See also

Ball Point Picking, Ball Line Picking, Ball Triangle Picking, Binomial Coefficient, Choose, Combination, Multichoose, Multiset, Permutation, String

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Cite this as:

Weisstein, Eric W. "Ball Picking." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BallPicking.html

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