Permutation & Combination Calculator
Calculate permutations and combinations for counting and probability problems.
A permutation and combination calculator computes the number of ways to arrange or select items from a set, with or without regard to order.
Examples
Permutation
Combination
Lottery
Frequently Asked Questions
When do I use permutation vs combination?
What is a factorial?
Why is C(n,r) always less than or equal to P(n,r)?
Quick Tips
- •Double-check your inputs — small errors lead to incorrect results.
- •Use permutations when order matters (rankings, passwords) and combinations when it does not (committees, lottery).
- •Remember that r cannot exceed n — you cannot choose more items than are available.
A permutation and combination calculator computes the number of ways to arrange or select items from a set, with or without regard to order.
How to Use This Calculator
Select permutation (order matters) or combination (order does not matter). Enter n (total items) and r (items chosen). The calculator computes both nPr and nCr.
Understanding the Formula
Permutation: P(n,r) = n!/(n-r)!; Combination: C(n,r) = n!/(r!(n-r)!)
Examples
Permutation
How many 3-letter codes from 26 letters (no repeat)? P(26,3) = 26×25×24 = 15,600
Combination
Choose 5 from 52 cards? C(52,5) = 2,598,960
Lottery
Pick 6 from 49? C(49,6) = 13,983,816
Frequently Asked Questions
When do I use permutation vs combination?
Use permutation when order matters (e.g., rankings, passwords). Use combination when order does not matter (e.g., selecting a committee, lottery numbers).
What is a factorial?
n! (n factorial) is the product of all positive integers up to n. For example, 5! = 5×4×3×2×1 = 120. By definition, 0! = 1.
Why is C(n,r) always less than or equal to P(n,r)?
Because P(n,r) counts every arrangement separately, while C(n,r) groups arrangements that use the same items. Specifically, P(n,r) = C(n,r) × r!.
Assumptions & Limitations
- Assumes items are distinct and selections are without replacement.
- Assumes exact input values; rounding in inputs propagates to results.
- Factorial results grow extremely fast and may lose precision for very large n.