Combination Calculator (nCr)
Combination Calculator (nCr)
The combination calculator finds how many ways you can choose r items from a group of n items when order does not matter. This is fundamental to probability and combinatorics.
Conversion Formula
C(n, r) = n! / (r! × (n - r)!). The calculation is optimized to avoid computing large factorials directly by using iterative multiplication.
Step-by-Step Examples
n = 52, r = 5 = 2,598,960
There are about 2.6 million possible 5-card poker hands from a standard deck.
n = 49, r = 6 = 13,983,816
The odds of winning a 6/49 lottery are 1 in ~14 million.
Frequently Asked Questions
What is a combination?
A combination is a selection of items where order does not matter. Choosing {A, B, C} is the same as choosing {C, A, B}.
What is the difference between combinations and permutations?
Combinations ignore order (selecting a team); permutations care about order (arranging a lineup). C(n,r) = P(n,r) / r!.
What does nCr mean?
nCr (read "n choose r") is the number of ways to choose r items from n items without regard to order.
Why do lottery odds use combinations?
Because the order in which lottery numbers are drawn does not matter. You win if you match the set, regardless of sequence.
What is C(n, 0)?
C(n, 0) = 1 for any n. There is exactly one way to choose nothing: choose nothing.