There are n! ways of arranging n distinct objects into an ordered sequence, permutations where n = r. The number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.
Permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor.
In Mathematics, a Permutation is defined as a mathematical concept that determines the number of possible arrangements for a specific set of elements. Therefore, it plays a big role in computer science, cryptography, and operations research.
What Is Permutation? A permutation is an arrangement, or listing, of objects in which the order is important. In previous lessons, we looked at examples of the number of permutations of n things taken n at a time. Permutation is used when we are counting without replacement and the order matters.