How is combination different from permutation?

Combination: order does not matter. Permutation: order matters. C(n,r) = P(n,r) / r!. So C(5,3) = P(5,3) / 6 = 60/6 = 10.

What are lottery odds?

Lottery odds are combinations. Picking 6 numbers from 49: C(49,6) = 13,983,816. So your odds of winning with one ticket are about 1 in 14 million.

What does C(n, 0) and C(n, n) equal?

Both equal 1. There is exactly 1 way to choose nothing (C(n,0)=1) and exactly 1 way to choose everything (C(n,n)=1).

Combination Calculator — nCr

The Combination Calculator computes C(n, r) — the number of ways to select r items from a set of n items, where order does NOT matter. Combinations are used in probability, lottery odds, card games, committee selection, and any scenario where you are choosing a group without regard to sequence.

Total items (n)

Items chosen (r)

How to Use This Calculator

1
Enter n — the total number of items in the set.
2
Enter r — the number of items you are selecting.
3
Click Calculate to see the number of combinations.

Frequently Asked Questions

A combination C(n,r) = n! / (r!(n-r)!) counts the ways to choose r items from n where order does not matter. Choosing 3 people from 10 for a team: C(10,3) = 120.

Related Calculators

🧮Permutation Calculator 🧮Factorial Calculator 🧮Probability Calculator