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Combination Formula Calculator

Formula

The formula to calculate the number of combinations (C) is:

$C(n, r) = \frac{n!}{r!(n - r)!}$

Where:

$C(n, r)$ is the number of combinations.
$n$ is the total number of items.
$r$ is the number of items to choose.
$n!$ is the factorial of $n$ .
$r!$ is the factorial of $r$ .
$(n - r)!$ is the factorial of $(n - r)$ .

Example

Let's say we have 5 items and we want to choose 3. Using the formula:

$C(5, 3) = \frac{5!}{3!(5 - 3)!} = \frac{5!}{3! \cdot 2!} = \frac{120}{6 \cdot 2} = 10$

So, the number of combinations is 10.

What is a Combination?

A combination is a selection of items from a larger set where the order of selection does not matter. It is used in various fields such as statistics, mathematics, and probability.