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 picking | name | symbol name | symbol ordered samples with replacement | string | power | n^k ordered sample without replacement | permutation | | _n P_k = (n!)/((n - k)!) unordered samples with replacement | multiset | multichoose | ((n k)) = (n + k - 1 k) unordered samples without replacement | combination | binomial coefficient, choose | _n C_k = (n k) = (n!)/(k!(n - k)!)

ball line picking | ball point picking | ball triangle picking | binomial coefficient | choose | combination | multichoose | multiset | permutation | string