# Combination Calculator

(also known as "n choose r" or binomial coefficient)

n  =

r  =

Solution

Combination C(n,r) = -

## Combination Formula

(Taking r at a time)

C(n,r) = n! /r!(n − r)!

## Combination Sample Problem

Chase has a 12 different colored marbles and he is going to take 3 of them, how many combinations exist given the scenario?

Using the formula:

C(n,r) = 12! /3!(12 − 3)!

In mathematical form, the problem looks like the following:
(12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (3 * 2 * 1) * (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)

**Note: the 9 in the last section of the problem comes from 12 - 3, as stated in the formula

And this is why we have a calculator to solve these problems, they can become very tedious, especially as the numbers get larger!

The answer is: 220, which means there are 220 different combinations for this problem.

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