Permutation & Combination Calculator

Calculate permutations and combinations for counting and probability problems.

Result

Fill in the fields above, then press Calculate.

A permutation and combination calculator computes the number of ways to arrange or select items from a set, with or without regard to order.

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.

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!.
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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.