5P3

5P3 is most commonly encountered in combinatorics as a shorthand for the number of permutations of five distinct items taken three at a time. It represents the value of the permutation function P(n, k) with n = 5 and k = 3, and is equal to n!/(n−k)!.

In this case, 5P3 = 5! / (5−3)! = 120 / 2 = 60. This counts all ordered arrangements of length 3 drawn from five items. For comparison, the number of 3-element combinations (order disregarded) is 5C3 = 10. If the items are labeled A, B, C, D, E, the 60 ordered triples include sequences such as ABC, ABD, ABE, and so on; the list would contain all 3-length sequences without repetition from the set.

The notation 5P3 appears in various texts and calculators in forms such as P(5,3) or _5P_3, with slight variations depending on the source. The concept generalizes to any nonnegative integers n and k with n ≥ k, where nPk denotes the number n!/(n−k)! and counts the number of ordered k-permutations of an n-element set. It is distinct from combinations, where the order of selection is not considered (nCk).

In other contexts, the string “5P3” may also appear as a product code, model number, or identifier specific to a domain, where its meaning is determined by the surrounding documentation.