Compute nPr (ordered arrangements) and nCr (unordered selections).
Permutations count ordered arrangements — picking a president, then a vice-president from the same group gives different results for different orders. Combinations count unordered selections — picking any 2 people for a committee, where the order you pick them in doesn't matter. nPr is always ≥ nCr for the same n and r.
You can't choose or arrange more items (r) than you have available (n) — for example, you can't select 5 people from a group of 3. The calculator requires r to be between 0 and n for the result to make sense.
Factorial-based values grow extremely fast — even n! for n around 170 already exceeds what standard double-precision numbers can represent. Capping n at 1000 keeps the iterative calculation numerically meaningful instead of overflowing to Infinity.