Permutation & Combination Calculator
Count arrangements (order matters) and selections (order doesn’t). Enter whole numbers with 0 ≤ r ≤ n ≤ 170.
⚠️ n is capped at 170 because 171! overflows JavaScript numbers (becomes Infinity). For n ≤ 170 the results are exact.
① Answer
Permutations nPr — order matters
ways to arrange r items from n
Combinations nCr — order doesn’t matter
ways to choose r items from n
② Steps
③ Why it works
Permutations count arrangements: order matters (1st, 2nd, 3rd place are different outcomes). Combinations count selections: order doesn’t matter (a team of Alice, Ben, Cara is one team no matter the order listed). Every combination of r items can be arranged r! ways, so nCr = nPr ÷ r! — that’s why combinations are always smaller.