Combination Calculator (nCr)
Calculate the number of combinations (nCr) for choosing r items from n items.
The Combination Calculator computes the number of ways to choose r items from a set of n items where order does not matter. This is written as C(n,r) or nCr.
Enter n (total items) and r (items to choose). The formula is nCr = n! / (r! * (n-r)!). Since factorials grow very fast, this calculator uses Stirling's approximation for large numbers.
Combinations are used in probability, lottery calculations, committee selection, and any scenario where you need to count selections without regard to arrangement order.
Frequently Asked Questions
What is the difference between combination and permutation?
Combinations do not consider order (choosing ABC = choosing BCA), while permutations treat different orders as different arrangements.
What is Stirling's approximation?
It is a formula to approximate large factorials: n! ~ sqrt(2*pi*n) * (n/e)^n. It is very accurate for n > 10.
How many lottery combinations are there?
For a 6/49 lottery: C(49,6) = 13,983,816 possible combinations.