Combination Calculator and Permutation Calculator

This combination calculator and permutation calculator finds how many ways to choose or arrange items. Use it for class, work, or quick checks. Pick a method, get a clear result with the formula shown. The Quick Reference explains the order rule at a glance.

How It Works

Enter n for the total number of items, and enter k for items to select. Use combinations when order has no effect. Use permutations when order matters. Combination formula: C(n, k) = n! divided by k! times the quantity n minus k factorial. Permutation formula: P(n, k) = n! divided by the quantity n minus k factorial. The result shows the formula and the final count, so you can check your reasoning.

Step-by-Step Instructions

Follow these steps to use the combination calculator or the permutation tool.

1. Type a whole number in n for total items.
2. Type a whole number in k for items you select.
3. Choose Calculate Combination to get C(n, k).
4. Choose Calculate Permutation to get P(n, k).
5. Read the formula and the result in the output box.
6. Read the short explanation shown under the result.

The calculator checks your input and gives guidance. Use whole numbers only. Set each value at least zero. Set k at most n. The explanation appears after a valid calculation.

Why Use the Combination Calculator?

You get combinations and permutations in one place. That saves time. Clear steps guide each choice. The displayed formula helps you learn as you compute.

It suits quick checks and study sessions. Verify homework and quiz prep. Plan seating, schedules, and small draws. You get the count you need without extra noise.

Useful Features at a Glance

• Quick Reference shows the difference between combinations and permutations with plain examples.
• Two clear modes for your task, so you pick the right method.
• Input checks guide valid entries, including k less than or equal to n.
• The output displays the formula and a neat number with commas.
• A short text explains the choice and gives a simple example.
• The calculator uses C(n, k) equals C(n, n minus k) to save steps.
• Works for k equal to zero and k equal to n as special cases.

Real-World Applications

• Form a team from a pool of candidates.
• Choose five cards from a deck where order has no effect.
• Count lottery pick outcomes for a given draw size.
• Arrange finalists into first, second, and third place.
• Set seat order for photos or stage spots.
• Assign roles to k people from a larger group.

A Quick Recap

1. Enter n and k.
2. Pick Combination or Permutation and click the button.
3. Read the result and the explanation.

The combination calculator keeps things quick and to the point. You see what matters, right away.

This tool helps with daily math tasks for school or work. Get clear counts, check your setup, and move on with confidence.