What is the formula for a permutation?

The formula for a permutation is correctly stated as nPr = n!/(n-r)!. This formula calculates the number of ways to arrange r items from a total of n items, where the order of selection matters. In this formula, n! represents the factorial of n, which is the product of all positive integers up to n. The term (n-r)! in the denominator accounts for the fact that we are only selecting r items out of the n, so the arrangements of the remaining (n-r) items do not need to be considered.

Permutations differ from combinations in that order is significant; hence, nPr reflects that by incorporating only the selected items into the arrangement rather than all available items. This understanding of the principles behind permutations is key in various mathematical contexts, such as probability and statistics.