Explanation:
Permutation
The 6 permutations of 3 balls
In mathematics, the notion of permutation is used with several slightly
different meanings, all related to the act of permuting (rearranging in an ordered
fashion) objects or values. Informally, a permutation of a set of objects is an
arrangement of those objects into a particular order. For example, there are
six permutations of the set {1,2,3}, namely (1,2,3), (1,3,2), (2,1,3),
(2,3,1), (3,1,2), and (3,2,1). One might define an anagram of a word as a permutation of
its letters. The study of permutations in this sense generally belongs to the
field of combinatorics.
The number of
permutations of n distinct objects is n×(n − 1)×(n − 2)×...×2×1, which
number is called "n factorial" and written "n!".
Generalities
In combinatorics
Permutations
of multisets
In combinatorics, a
permutation is usually understood to be a sequence containing each element from a finite
set once, and only once. The concept of sequence is distinct from that of a set, in that the elements of a
sequence appear in some order: the sequence has a first element (unless it is
empty), a second element (unless its length is less than 2), and so on. In
contrast, the elements in a set have no order; {1, 2, 3} and {3, 2, 1} are
different ways to denote the same set. In this sense a permutation of a finite
set S of n elements is equivalent to a bijection
from {1, 2, ..., n} to S (in which any i is mapped to the i-th element of the sequence),
or to a choice of a total
ordering on S (for which x < y if x
comes before y in the sequence). In this sense there
are also n! Permutations of S.
There is also a weaker meaning of the term "permutation"
that is sometimes used in elementary combinatorics texts, designating those
sequences in which no element occurs more than once, but without the
requirement to use all elements from a given set. Indeed this use often involves
considering sequences of a fixed length k of elements taken from a given set of
size n. These objects are
also known as sequences
without repetition, a term that avoids confusion with the other, more
common, meanings of "permutation".
The number of such k-permutations
of n is denoted variously by such symbols
as _{n} P_{k}, ^{n}P_{k}, P_{n}_{,k},
or P(n,k),
and its value is given by the product
which is 0 when k > n,
and otherwise is equal to
(Our solved example in mathguru.com uses
this concept)
http://en.wikipedia.org/wiki/Permutation
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