Free Permutation Combination Calculator Online
This free online permutation combination calculator computes nPr and nCr values with step-by-step formulas for counting arrangements and selections.
Inputs
Permutations nPr
Enter n and r above
How the Permutation Combination Calculator Works
The permutation combination calculator takes two inputs: n (total items) and r (items to choose). It computes both nPr (permutations) and nCr (combinations) using factorial formulas. The permutation combination calculator shows the full formula breakdown.
For n=10, r=3: nPr = 10!/(10−3)! = 10×9×8 = 720 arrangements. nCr = 10!/(3!×7!) = 720/6 = 120 combinations. The permutation combination calculator computes both instantly.
The permutation combination calculator also shows n! and (n−r)! values for reference. These factorials are the building blocks of both formulas and help you understand the calculation steps.
Permutations vs Combinations
Use permutations when order matters. Arranging 3 books on a shelf from 10 books: 10P3 = 720 different arrangements. Use the permutation combination calculator for this type of problem.
Use combinations when order does not matter. Choosing 3 team members from 10 people: 10C3 = 120 possible teams. The permutation combination calculator clearly separates these two types of counting.
Real examples: lottery numbers (combinations — order irrelevant), PIN codes (permutations — order matters), committee selection (combinations), race finishing order (permutations). The permutation combination calculator handles all these scenarios.
Tips for Using the Permutation Combination Calculator
Does Order Matter?
If yes, use nPr. If no, use nCr. The permutation combination calculator shows both so you can pick the right one.
r Cannot Exceed n
You cannot choose more items than available. The permutation combination calculator validates this constraint.
nCr = nPr / r!
Combinations are always fewer than permutations by a factor of r!. The permutation combination calculator shows this relationship.
Large n Values
Factorials grow very fast. The permutation combination calculator handles large values accurately within JavaScript number limits.
Frequently Asked Questions
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