Combination Calculator (nCr and nPr)

Your details

The size of the full set you are choosing from.
How many items you select from the set.
Choose "Both" for the standard without-repetition formulas. Switch to see results when items can be reused.
When on, the calculator shows 1 / nCr -- the chance that one randomly chosen group matches a specific target combination (e.g. a lottery ticket).
Combinations (nCr)
15
Permutations (nPr)30
Combinations (nCr)15
Permutations (nPr)30

Choosing 2 from 6: 15 combinations, 30 permutations.

  • There are 15 ways to choose 2 of 6 items when order does not matter (combinations).
  • There are 30 ways when order does matter (permutations).
  • Permutations are 2 times larger because each combination can be arranged in 2! = 2 different orders.

Next stepUse combinations for lottery or committee picks; use permutations for ordered passwords, podium finishes, or seating.

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