4×3×2×1

The expression 4×3×2×1 is the product of the four positive integers from 4 down to 1. It is standardly written as 4!, pronounced “four factorial,” and it equals 24. By definition, n! = n×(n−1)×...×1 for nonnegative integers.

In combinatorics, 4! counts the number of ways to arrange four distinct items in a sequence, i.e., the number of permutations of four objects. More generally, n! counts the number of permutations of n distinct items; factorials also appear in formulas for binomial coefficients and in many probability calculations.

The prime factorization of 24 is 2^3 × 3. It is the product of the first four positive integers and is even. The factorial function extends beyond integers through the gamma function, with Γ(n+1) = n!, providing a continuous extension of the factorial to non-integer values.

Notes: 4! and the related factorial notation are foundational in areas such as combinatorics, algebra, and computer science. The concept also serves as a building block for more complex counting and probability problems, including permutations, combinations, and series expansions.