Combinations Calculator: Clear Results and Steps

Use this combinations calculator to count choices where order is ignored. It suits study and work plus quick checks. You get the answer and the steps. The page also explains combinations versus permutations. You will see a link for a permutations calculator.

How It Works

The formula is C of n r equals n factorial divided by r factorial times n minus r factorial. Factorial means the product of all whole numbers from a value down to one. This combinations calculator applies that formula and shows each step.

• n means the total number of items in your set.
• r means how many items you choose from that set.
• Type whole numbers only for both fields.
• Use r less than or equal to n.
• Use n up to 170 to keep values safe.

Combinations and permutations serve different goals, so the page gives a quick guide.

• Combinations count selections where order is ignored, so AB and BA count as the same.
• Permutations count arrangements where order matters, so AB and BA count as different.

Step-by-Step Instructions

1. Enter the total number of items in the n field.
2. Enter how many items to choose in the r field.
3. Click Calculate Combinations or press Enter.
4. Read the result line with the total count of combinations.
5. Review the formula steps and the factorial breakdown below the result.
6. Check the example line that uses your numbers in plain words.

You now have the count and the math that produced it.

Why Use This Tool

Fast results help you plan and learn. Clear steps show how the number was computed. Input checks flag values outside the rules. Large counts display with commas for easy reading. This combinations calculator supports quick study and teaching.

Benefits for Everyday Use

Here are common cases where a combinations calculator helps.

• Choose three team members from ten people.
• Form a four person committee from twelve staff.
• Select lottery numbers where order does not matter.
• Count five card poker hands from a fifty two card deck.
• Pick a sample of twenty items from a batch of five hundred.
• Build a study set from a pool of practice questions.

Math at Your Fingertips

The output shows the total number of combinations for your entries. It repeats your n and r and prints the formula line. You also see the factorial values used in the calculation. The page then shows the final simplified result.

Small inputs display the full multiplication for each factorial. Large inputs display a shorter product with the final value. Big numbers use commas so the count reads cleanly at a glance.

• Enter whole numbers for both n and r.
• Use zero or positive values for each field.
• Keep r less than or equal to n.
• Keep n at one hundred seventy or less to avoid overflow.
• Press Enter to run the calculation without clicking the button.
• See the short note on permutations and the link near the inputs.

Try the combinations calculator on your next problem. Enter n and r and get a clear answer fast. Learn the method while you work through real tasks.