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.