A permutation is an ordered arrangement of objects from a group without repetitions. For example, there are six ways to order the letters abc without repeating a letter. The six permutations are abc, acb, bac, bca, cab, cba.

Use the Permutation function to find the number of permutations of n items chosen k at a time. Permutations are used to calculate the probability of an event in an experiment with only two possible outcomes (binomial experiment).

Syntax

PERMUTATIONS (number of items, number to choose)

Specify a number or column for the number of items and the number to choose. The number of items must be greater than or equal to 1, and the number to choose must be greater than or equal to 0.

Example

Suppose 10 people enter a contest. How many different ways can 1st, 2nd, and 3rd place be awarded when order is important?

Calculation expression

Result

PERMUTATIONS (10,3)

720

Formula

Usually, the number of permutation of n items chosen k at a time is:

Other uses

Permutations can also be used to determine the number of possible ways to order a group of letters or digits, which has applications in coding. Combinations and permutations, known as combinatorics, play an important role in network engineering, computer science (cryptography), molecular biology (pattern analysis), and other fields.