Seating Arrangements Calculator

About this calculator

Seating r people chosen from a group of n in a row, where order matters, is counted by the permutation formula P(n,r) = n! / (n−r)! — the number of ways to fill the first seat times the ways to fill the second given the first is taken, and so on, for r seats. When r equals n, this reduces to n!, every arrangement of the whole group.

Teachers use this calculator to demonstrate permutations concretely in combinatorics lessons, event and wedding planners use it when working out how many distinct seating orders are possible for a head table, and students use it to check homework problems that ask for the number of ways to arrange people or objects in a line.