Permutation and Combination Calculator

Defining 'n' and 'r'

The logic is based on two standard variables. Total Items (n) represents the complete set of objects you are choosing from. Items Chosen (r) is the subset you are selecting. For instance, if you are picking a 3-person committee from a group of 10, 'n' is 10 and 'r' is 3. Hitting Run applies the standard $nPr$ and $nCr$ formulas to these inputs simultaneously.

Permutations vs. Combinations

The output area explicitly labels the results for both methods to prevent confusion:

• Permutations ($nPr$): Used when sequence is important, such as cracking a padlock code or assigning 1st, 2nd, and 3rd place medals.
• Combinations ($nCr$): Used when the sequence is irrelevant, such as dealing a hand of poker or forming a generic project group.

Once you know the total number of combinations for your scenario, you can plug that figure into the Probability Calculator as your "Total Possible Outcomes" to find the exact odds of a specific event. If your mathematical model requires checking the divisibility of these large output groups, the Prime Number Checker can be used to evaluate the resulting numbers.

Handling Large Values

Because factorial math scales aggressively, calculating something like 100 choose 5 involves incredibly large intermediary numbers. This calculator uses precision math to output the final results accurately. You can Copy the exact figure to your clipboard, or use Reset to clear the 'n' and 'r' fields for your next counting problem.

Frequently Asked Questions