Combination and Permutation Calculator

How to Use?

1. 1

   Choose what you are counting

   Select Combination when order does not matter, Permutation when it does, or Factorial to count arrangements of everything at once. The swap test above the form settles the choice: if rearranging the picked items changes the outcome, use Permutation.

2. 2

   Enter the pool and the pick

   Type the pool size n and the pick size k as whole numbers – 49 and 6 for the lottery draw, 10 and 3 for the podium. Inputs are validated as whole numbers, and k beyond n is flagged as an error in the without-repetition setting.

3. 3

   Set the repetition rule

   Keep Without Repetition for deals, hands, and draws from a single pool. Switch to With Repetition for passwords, sequences, and scoops – anything where an item can be picked again.

4. 4

   Read the result

   The exact count appears with its formula label, such as C(49, 6). Digit grouping keeps large counts readable – 13,983,816 rather than a scientific blob.

5. 5

   Compare the companion counts

   The other-count output shows what the same n and k give under the opposite order rule, and the repetition-variant output shows the opposite repetition setting. The premiums that order and repetition charge are visible without a second calculation.

6. 6

   Check Pascal’s row

   The bar chart in the results plots row n of Pascal’s triangle with your k highlighted, showing how your selection sits within the row’s full landscape of subset sizes.

7. 7

   Apply the one-in-X line

   When outcomes are equally likely, the probability line converts your count to odds of a single specific selection – the lottery’s 1 in 13,983,816 directly.