*Also known as, or referred to as "n choose r" or binomial coefficient
n =
r =
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.