Calculate nPr — the number of ordered arrangements of r items chosen from n items.
| n | r | nPr | Meaning |
|---|---|---|---|
| 5 | 2 | 20 | 5 items, pick 2 ordered |
| 10 | 3 | 720 | 10 items, pick 3 ordered |
| 52 | 5 | 311,875,200 | Card hands ordered |
A permutation is an ordered arrangement of items from a set. Unlike combinations, the order of selection matters in permutations. For example, the arrangements ABC and BAC are considered different permutations. Permutations are used in probability, statistics, cryptography, and everyday scenarios like ranking, scheduling, and security codes.
The key difference is order. In a permutation, order matters — choosing A then B is different from choosing B then A. In a combination, order does not matter — {A, B} is the same as {B, A}. For example, a 3-digit PIN where order matters is a permutation. Choosing 3 toppings for a pizza where order does not matter is a combination.
n! (n factorial) is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials grow extremely fast — 20! is already over 2 quintillion.
Without repetition, r cannot exceed n because you cannot arrange more items than you have. With repetition allowed, r can exceed n since items can be reused.
P(n, 0) = 1 for any value of n. There is exactly one way to arrange zero items — the empty arrangement.