Combinatorics is the branch of mathematics that deals with arrangements of objects, usually finite in number. The term arrangement encompasses, among other possibilities, selection, grouping, combination, ordering or placement, subject to various constraints.
Elementary combinatorial theory concerns permutations and combinations. For example, the number of permutations or orderings of n objects is n! = n(n − 1) ... (2)(1), and the number of combinations of n objects taken k at a time is given by the binomial coefficient (n k) = n!/[k!(n − k)!]. In order to compute the probability of throwing a 7 with two dice, or of drawing an inside straight at poker, one must be able to count permutations and combinations, as well as other types of arrangements. Indeed, combinatorics is said to have originated with investigations of games of chance. Combinatorial counting theory is the foundation of discrete probability theory as we know it today.
Experimental design provides the motivation for...
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Lawler, E.L. (2001). Combinatorics . In: Gass, S.I., Harris, C.M. (eds) Encyclopedia of Operations Research and Management Science. Springer, New York, NY. https://doi.org/10.1007/1-4020-0611-X_132
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