Enter n and r and instantly get the number of permutations, combinations, and both factorials — with the working shown.
Permutation & Combination Calculator
How It’s Calculated
nPr = n! / (n−r)! counts arrangements where order matters. nCr = n! / (r!(n−r)!) counts selections where order doesn’t matter — so nCr is always nPr divided by r! (the number of ways to reorder each selected group). This calculator uses a multiplicative formula rather than raw factorials, so it stays accurate even for larger values of n.
Worked Example
For n = 6, r = 3: 6P3 = 6×5×4 = 120 (arranging 3 of 6 items in order). 6C3 = 120 / 3! = 120/6 = 20 (choosing 3 of 6 items, order irrelevant).
Frequently Asked Questions
Q: How do I know whether a question needs nPr or nCr?
Ask whether order matters. Arranging people in a queue, or forming a 3-digit code: order matters, use nPr. Choosing a committee, or picking a hand of cards: order doesn’t matter, use nCr.
Q: Why is nCr always smaller than or equal to nPr?
Because nCr groups together all the different orderings of the same selection into a single count — nCr = nPr ÷ r!.
This is exactly the distinction Daniel Sir drills into every 1st PUC batch on Permutations & Combinations. See how Daniel Classes teaches 1st and 2nd PUC Mathematics →