Combination Calculator (nCr)

How to use this calculator

Enter the total items and how many are chosen. You get the number of possible combinations and the chance of picking one specific combination.

Formula

nCr = n! ÷ ( r! × (n − r)! )

Worked examples

• 6/49 lottery: 49C6 = 13,983,816
• Pizza: choose 3 toppings from 10 → 120 combinations
• Teams: pick 5 players from 12 → 792 teams

Pascal’s triangle

nCr values form Pascal’s triangle — each number is the sum of the two above it. They are also the coefficients in (a + b)ⁿ.

Frequently asked questions

What is a combination?

A selection where order doesn't matter, such as choosing 3 toppings from 10.

What is the formula?

nCr = n! ÷ (r! (n − r)!).

What are the odds of winning a 6/49 lottery?

1 in 13,983,816 for the jackpot.

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