Search results
Results from the WOW.Com Content Network
In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations).For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange.
One must divide the number of combinations producing the given result by the total number of possible combinations (for example, () =,,).The numerator equates to the number of ways to select the winning numbers multiplied by the number of ways to select the losing numbers.
A k-combination of a set S is a subset of S with k (distinct) elements. The main purpose of the combinatorial number system is to provide a representation, each by a single number, of all () possible k-combinations of a set S of n elements.
Multiple points on a line imply multiple possible combinations (blue). Only lines with n = 1 or 3 have no points (red). In mathematics , the coin problem (also referred to as the Frobenius coin problem or Frobenius problem , after the mathematician Ferdinand Frobenius ) is a mathematical problem that asks for the largest monetary amount that ...
The same argument shows that the number of compositions of n into exactly k parts (a k-composition) is given by the binomial coefficient (). Note that by summing over all possible numbers of parts we recover 2 n−1 as the total number of compositions of n:
The number of derangements of a set of size n is known as the subfactorial of n or the n th derangement number or n th de Montmort number (after Pierre Remond de Montmort). Notations for subfactorials in common use include !n, D n, d n, or n¡ . [a] [1] [2] For n > 0 , the subfactorial !n equals the nearest integer to n!/e, where n!
3. As the n digit multiplication problem grows to ever larger numbers, the number of possible combinations one can use to reach the same answer grows as well; meaning the user can pick and choose the easiest and fastest route to reach the answer to each multiplication problem according to their own specific needs at the time.
A map of the 24 permutations and the 23 swaps used in Heap's algorithm permuting the four letters A (amber), B (blue), C (cyan) and D (dark red) Wheel diagram of all permutations of length = generated by Heap's algorithm, where each permutation is color-coded (1=blue, 2=green, 3=yellow, 4=red).