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The set of all k-combinations of a set S is often denoted by (). A combination is a selection of n things taken k at a time without repetition. To refer to combinations in which repetition is allowed, the terms k-combination with repetition, k-multiset, [2] or k-selection, [3] are often used. [4]
In combinatorial mathematics, a partial permutation, or sequence without repetition, on a finite set S is a bijection between two specified subsets of S. That is, it is defined by two subsets U and V of equal size, and a one-to-one mapping from U to V. Equivalently, it is a partial function on S that can be extended to a permutation. [1] [2]
Permutations without repetition on the left, with repetition to their right. If M is a finite multiset, then a multiset permutation is an ordered arrangement of elements of M in which each element appears a number of times equal exactly to its multiplicity in M. An anagram of a word having some repeated letters is an example of a multiset ...
If must be injective, then the selection must involve n distinct elements of X, so it is a subset of X of size n, also called an n-combination. Without the requirement, one and the same element of X may occur multiple times in the selection, and the result is a multiset of size n of elements from X, also called an n-multicombination or n ...
Combinations and permutations in the mathematical sense are described in several articles. Described together, in-depth: Twelvefold way; Explained separately in a more accessible way: Combination; Permutation; For meanings outside of mathematics, please see both words’ disambiguation pages: Combination (disambiguation) Permutation ...
A pair will be the same no matter the order of the two people. A handshake must be carried out by two different people (no repetition). So, it is required to select an ordered sample of 2 elements out of a set of 50 elements, in which repetition is not allowed. That is all we need to know to choose the right operation, and the result is:
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Lottery mathematics is used to calculate probabilities of winning or losing a lottery game. It is based primarily on combinatorics , particularly the twelvefold way and combinations without replacement .