The number of valid seating arrangements is $\boxed{48}$.

Sun, 03 May 2026 22:07:10 +0000

The Number of Valid Seating Arrangements Is $oxed{48}$: A Simple Combinatorics Breakdown When solving seating arrangement problems, combinatorics provides a powerful toolkit to determine how many distinct ways people—or objects—can be arranged according to given constraints. One classic and elegant example is determining the number of valid seating arrangements where exactly 48 different valid configurations exist. This article explores how this number arises using permutations and logical constraints. ### Understanding Seating Arrangements At its core, a seating arrangement involves placing people or items in a sequence—such as around a circular or linear table—where the order matters. For n distinct people, the total number of possible arrangements is typically n! (n factorial), reflecting all possible orderings.