Number of Combinations With Repetition
See also: Multiset coefficientA k-combination with repetitions, or k-multicombination, or multiset of size k from a set S is given by a sequence of k not necessarily distinct elements of S, where order is not taken into account: two sequences of which one can be obtained from the other by permuting the terms define the same multiset. In other words, the number of ways to sample k elements from a set of n elements allowing for duplicates (i.e., with replacement) but disregarding different orderings (e.g. {2,1,2} = {1,2,2}). If S has n elements, the number of such k-multicombinations is also given by a binomial coefficient, namely by
(the case where both n and k are zero is special; the correct value 1 (for the empty 0-multicombination) is given by left hand side, but not by the right hand side ). This follows from a clever representation of such combinations with just two symbols (see Stars and bars (combinatorics)).
Read more about this topic: Combination
Famous quotes containing the words number of, number, combinations and/or repetition:
“I will not adopt that ungenerous and impolitic custom so common with novel writers, of degrading by their contemptuous censure the very performances, to the number of which they are themselves addingjoining with their greatest enemies in bestowing the harshest epithets on such works, and scarcely ever permitting them to be read by their own heroine, who, if she accidentally take up a novel, is sure to turn over its insipid leaves with disgust.”
—Jane Austen (17751817)
“In a number of other cultures, fathers are not relegated to babysitter status, nor is their ability to be primary nurturers so readily dismissed.... We have evidence that in our own society men can rear and nurture their children competently and that mens methods, although different from those of women, are imaginative and constructive.”
—Kyle D. Pruett (20th century)
“...black women write differently from white women. This is the most marked difference of all those combinations of black and white, male and female. Its not so much that women write differently from men, but that black women write differently from white women. Black men dont write very differently from white men.”
—Toni Morrison (b. 1931)
“Between repetition and forgetting, it is a marvel that a new thought ever struggles into existence.”
—Mason Cooley (b. 1927)