How to Put Combinations in a Calculator

This guide shows you how to calculate combinations (nCr) on a standard scientific calculator, a graphing calculator, and a basic online calculator. You’ll learn the button sequences, the formula behind it, and how to avoid the most common mistakes. No special equipment is needed beyond the calculator you already have.

Formula

The number of combinations (nCr) tells you how many ways you can choose r items from a set of n items, where the order does not matter. The formula is:

nCr = n! / [ r! × (n − r)! ]

• n = total number of items (must be a non-negative integer)
• r = number of items chosen (must be a non-negative integer, r ≤ n)
• ! = factorial (e.g., 5! = 5 × 4 × 3 × 2 × 1 = 120)

For example, choosing 3 books from a shelf of 10 gives 10C3 = 120 possible sets.

Worked Example

Using the default values from the calculator above: n = 10, r = 3.

Step 1: Compute the factorials.

• 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800
• 3! = 3 × 2 × 1 = 6
• (10 − 3)! = 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040

Step 2: Plug into the formula.

10C3 = 3,628,800 / (6 × 5,040) = 3,628,800 / 30,240 = 120

So the calculator returns 120 combinations.

Step-by-Step: Using a Scientific Calculator

1. Turn on the calculator and clear the screen (press AC or C).
2. Enter the value of n (the total number of items). For example, press 1 then 0 for 10.
3. Look for the nCr button. On most scientific calculators, it is a secondary function above the + or ÷ key, often printed in yellow or blue. To access it, press the SHIFT or 2ndF key first, then the key with nCr.
4. After pressing nCr, enter the value of r (the number chosen). For example, press 3.
5. Press the = button. The display shows the result: 120.

Step-by-Step: Using a Graphing Calculator (TI-84/83)

1. Turn on the calculator.
2. Enter the value of n (e.g., 10).
3. Press the MATH key.
4. Use the arrow keys to scroll to the PRB (probability) menu.
5. Select option 3: nCr and press ENTER.
6. Enter the value of r (e.g., 3).
7. Press ENTER again. The result appears: 120.

Step-by-Step: Using an Online Calculator

1. Open a web browser and go to a combination calculator website (like this-calculator.com).
2. Find the input field labeled n (total items) and type your number.
3. Find the input field labeled r (chosen items) and type your number.
4. Click the Calculate button. The result is displayed instantly.

Common Mistakes

• Confusing nCr with nPr: nCr (combinations) ignores order; nPr (permutations) counts order. For example, choosing 2 letters from A, B, C: combinations give AB, AC, BC (3), while permutations give AB, BA, AC, CA, BC, CB (6).
• Entering n and r in the wrong order: Make sure you input the total first, then the chosen number. Swapping them gives a different result (unless n = r).
• Using a negative or decimal number: n and r must be whole numbers (non-negative integers). Some calculators will give an error or a nonsensical result if you try decimals.
• Forgetting to use SHIFT/2ndF on scientific calculators: If you press the nCr key without the shift, you might get a different function (like the plus sign).

Tips

• Check if your calculator has a dedicated nCr button. If not, you can compute it manually using the factorial function (!) and the formula above.
• For large n (like n = 50), the result can be huge. Many calculators display in scientific notation (e.g., 1.26E14). That’s fine—just interpret it as 1.26 × 10^14.
• Use the combination formula when the order doesn’t matter: lottery numbers, choosing a committee, selecting toppings on a pizza.
• If your calculator has a nPr button nearby, double-check you pressed nCr, not nPr.

Troubleshooting

• Getting an error message: Make sure r ≤ n and both are non-negative integers. If you used decimals, clear and re-enter whole numbers.
• Result seems too small or too large: Check if you accidentally used nPr instead of nCr. nPr is always larger (or equal) than nCr for the same n and r.
• No nCr button visible: Look for a second function. On many Casio models, it’s above the ÷ key; on TI models, it’s in the MATH menu under PRB.
• The calculator shows a fraction or decimal: Some calculators output in fraction form. Press the S↔D (standard to decimal) button to convert to a decimal if needed.
• Online calculator gives a different result: Verify you entered n and r correctly. Also, make sure the website uses the same definition (some might use permutations by default).

Frequently Asked Questions

Q: What is the difference between a combination and a permutation?
A: A combination (nCr) counts selections where order doesn’t matter. A permutation (nPr) counts arrangements where order does matter. For example, choosing 2 people from a group of 3: combinations give 3 pairs, permutations give 6 ordered pairs.

Q: Can I use nCr for large numbers like n=100?
A: Yes, but the result will be astronomically large. Most calculators handle it using scientific notation. For exact integer values, you may need a computer or a specialized calculator.

Q: What if r is greater than n?
A: The result is 0, because you can’t choose more items than exist. Most calculators will show an error or 0. Always check that r ≤ n.

Q: Is nCr the same as the binomial coefficient?
A: Yes, nCr is exactly the binomial coefficient, often written as (n choose r). It appears in the binomial theorem and probability calculations.

Q: How do I calculate combinations without the nCr button?
A: Use the formula: n! / (r! × (n−r)!). On a calculator, you can compute factorials using the ! key, then do the division. For example, 10C3 = 10! / (3! × 7!) = 3,628,800 / (6 × 5,040) = 120.

Q: Why does my calculator show a decimal like 120.0 instead of 120?
A: That’s normal; many calculators display the result with a decimal point to indicate it’s a floating-point number. The value is still the integer 120.

Related

• Combination on Scientific Calculator: How to Do nCr
• Combination Rule Calculator: How to Use It
• Combination Sum Calculator: Find All Combos

in n | Total items (n) | items | 10 | 0
in r | Chosen (r) | items | 3 | 0
out comb | Combinations (nCr) | - | ncr(n, r) | 0
out perm | Permutations (nPr) | - | npr(n, r) | 0