Number of ways a subset of objects can be selected from a given set of objects. In a permutation, order is important; in a combination, it is not. Thus, there are six permutations of the letters A, B, C selected two at a time (AB, AC, BC, BA, CA, CB) yet only three combinations (AB, AC, BC). The number of permutations of r objects chosen from a set of n objects, expressed in factorial notation, is n! (n -r)! The number of combinations is n! [r!(n -r)!]. The (r + 1)st coefficient in the binomial expansion of (x + y)^n coincides with the combination of n objects chosen r at a time (see binomial theorem). Probability theory evolved from the study of gambling, including figuring out combinations of playing cards or permutations of win-place-show possibilities in a horse race, and such counting methods played an important role in its development in the 17th century
The number of ways of selecting objects from n distinguishable objects without replacement when order of selection is important nPr =n (n-1) (n-2) (n-r+1)
Given an ordered set of elements, a permutation is a reordering of that set where each element appears exactly once For example, "egam" is a permutation of "game", or "2431" is a permutation of "1234"
A permutation is a way to order a set of things For example, if your set is the letters in the word WHO, then one other ordering would be WOH Here are all the possible orderings of the letters in the word WHO: WHO WOH HWO HOW OWH OHW There are 6 different ways to order the letters in the word WHO To learn more about permutations, see the permutation notes
A permutation can be thought of in two ways: in passive form, it is an arrangement of the elements of a set in order; in active form, it is a one-to-one and onto function from the set to itself (so that the passive form is the image of the "natural" order of the set) For example, the permutation whose passive form is (2,4,1,3) is, in active form the function which maps 1 to 2, 2 to 4, 3 to 1, 4 to 3 Permutations in active form are functions and can be composed This composition is the group operation in the symmetric group
A permutation is one of the ways in which a number of things can be ordered or arranged. Variation among humans is limited to the possible permutations of our genes. one of the different ways in which a number of things can be arranged (permutacion, from , from permutare )
A situation in which order matters In general, the number of permutations of n things taken m at a time is denoted asP(n,m) and is calculated by evaluating the expression [DMTA, p 275]
A permutation of a set is an arrangement of the elements of the set in some order If the set has n things in it, there are n! different orderings of its elements For the first element in an ordering, there are n possible choices, for the second, there remain n-1 possible choices, for the third, there are n-2, etc , and for the nth element of the ordering, there is a single choice remaining By the fundamental rule of counting, the total number of sequences is thus n×(n-1)×(n-2)× ×1 Similarly, the number of orderings of length k one can form from n>=k things is n×(n-1)×(n-2)× ×(n-k+1) = n!/(n-k)! This is denoted nPk, the number of permutations of n things taken k at a time C f combinations
A a particular ordering of a set of objects For example, given the set {1, 2, 3}, there are six permutations: {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, and {3, 2, 1}