Permutation & Combination Calculator
Calculate nPr (permutations) and nCr (combinations).
Assumptions used in this calculation
- No repetition: Assumes items are chosen without repetition/replacement and are distinguishable, the standard nPr/nCr definitions.
About this calculator
Counting how many ways you can arrange or select items from a group requires factorials that get enormous fast (10! is already over 3.6 million), and mixing up whether order matters is the single most common mistake in combinatorics problems, whether you're arranging race finishers or picking a committee. This calculator computes both nPr, the number of ways to arrange r items chosen from n where order matters (n! ÷ (n−r)!), like assigning 1st, 2nd and 3rd place, and nCr, the number of ways to choose r items from n where order doesn't matter (n! ÷ (r! × (n−r)!)), like selecting an unordered group. Because nCr always divides nPr by r! to collapse the redundant orderings within each group, the calculator returns both values together so you can see the relationship directly. It returns 0 for both when r exceeds n, since you can't select more items than exist in the set. That avoids computing large factorials by hand and avoids the order-matters mix-up.
Worked example
n=5, r=3
Result: nPr = 60, nCr = 10
Was this helpful?