Combinations Permutations

Calculate combinations and permutations.

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Results

Permutations P(n,r) —
Combinations C(n,r) —

What is this calculator for?

The Combinations Permutations provides quick and accurate combinations permutations calculations for everyday planning, analysis, and decision-making.

How to Use This Calculator

Enter the values below, then press Calculate (or press Enter). The calculator updates your results instantly. Try different values to see how your inputs change the outcome.

  1. Total Items (n) — enter a numeric amount. A typical Total Items (n) would be 10.
  2. Select Items (r) — enter a numeric amount. A typical Select Items (r) would be 3.
  3. Review your results — the key output is highlighted, with supporting figures below.

What You'll Need

Total Items (n)
a numeric amount range 0–100 · required
Select Items (r)
a numeric amount range 0–100 · required

About This Calculator

The Combinations Permutations computes the number of ways to select and arrange items from a set, supporting combinations permutations scenarios. Permutations count arrangements where order matters, while combinations count groups where order does not matter. These calculations are essential in probability theory, statistical analysis, lottery odds, quality control, and many other fields where counting possibilities is required.

Enter the total number of items in your set and the number of items you want to select. The Combinations Permutations instantly calculates both permutations and combinations, giving you the complete picture for combinations permutations probability and counting problems. The results update immediately as you adjust either value.

The Combinations Permutations handles both permutations and combinations simultaneously, giving you a complete picture of your counting problem. Understanding the difference between ordered and unordered selections is crucial in combinations permutations probability and statistics work. This calculator helps you avoid the common mistake of using the wrong formula for your specific scenario.

Formula

P(n,r) = n! / (n-r)! C(n,r) = n! / (r! * (n-r)!)

Worked Examples

Combinations Permutations Selection

Permutations: 720, Combinations: 120

Frequently Asked Questions

When should I use permutations versus combinations for combinations permutations?
Use permutations when the order of selection matters, such as arranging items, forming passwords, or ranking candidates. Use combinations when order does not matter, such as selecting a committee, choosing lottery numbers, or picking items from a menu. The key question is whether rearranging the same items creates a different combinations permutations outcome.
Why are permutations always greater than or equal to combinations for combinations permutations?
Permutations count every possible arrangement of the selected items, while combinations count each unique group only once. Since each combination of r items can be arranged in r factorial different ways, permutations equal combinations multiplied by r factorial. This relationship is fundamental to combinations permutations counting problems.
What is the difference between permutations with and without repetition for combinations permutations?
Without repetition, each item can be selected only once. With repetition, items can be reused. For example, a 4-digit PIN allows repetition, while selecting 4 cards from a deck does not. The Combinations Permutations computes permutations and combinations without repetition for accurate combinations permutations results.
How are permutations and combinations used in combinations permutations probability?
To find the probability of a specific outcome, divide the number of favorable arrangements by the total number of possible arrangements. This approach solves problems ranging from card games to quality control, making combinations permutations probability calculations systematic and accurate.
Can I use the Combinations Permutations for lottery odds calculations?
Yes, lottery odds are calculated using combinations. For example, choosing 6 numbers from 49 gives over 13.9 million possible combinations, meaning the odds of matching all six are approximately 1 in 14 million. Use the combinations result to understand your chances in any combinations permutations lottery or random selection scenario.