Probability Solver

Calculate combinations and permutations instantly with professional formatting.

Total Items (n)

Chosen Items (r)

Combinations

120

The number of ways to choose 3 items from 10 without regard to order.

Permutations

720

The number of ways to arrange 3 items from 10 where order matters.

Probability FAQ

Combinations (nCr) are used when the order does not matter (e.g., picking a committee). Permutations (nPr) are used when the order does matter (e.g., a race or a password).

In mathematics, the empty product is defined as 1. This convention makes many formulas (like nCr) work consistently for all cases.

The calculator works for any non-negative integers where n ≥ r. For very large numbers, results may be shown in scientific notation.