Combinations & Permutations Calculator
How many ways to choose r items from n (order ignored) or arrange them (order matters).
Combinations vs. permutations
nCr = n! / (r!(n-r)!) nPr = n! / (n-r)!
Use combinations when order doesn't matter (a lottery pick, a committee) and permutations when it does (a podium, a password). From 10 people, there are 120 possible committees of 3 but 720 possible gold-silver-bronze outcomes: exactly 3! = 6 times more, one for each ordering of the same trio.
These numbers get big fast
52 cards can be shuffled into 52! orders, a number with 68 digits. Results beyond about 15 digits are shown in scientific notation; the leading digits are exact enough for any counting argument, but for exact arithmetic at that size you want a computer algebra system.