Calculate factorials, permutations, and combinations with ease. Supports large integer arithmetic for accurate results.
Factorial (n!) is the product of all positive integers less than or equal to n. E.g., 5! = 5×4×3×2×1 = 120. 0! is defined as 1.
P(n,r) counts the number of ways to arrange r items from n distinct items, where order matters. Formula: P(n,r) = n!/(n-r)!
C(n,r) counts the number of ways to select r items from n items, where order doesn't matter. Formula: C(n,r) = n!/[r!(n-r)!].
0! = 1 is a mathematical convention that ensures formulas like permutations and combinations work correctly at boundary values.