Number of Combinations Calculator

Formula

The formula to calculate the Number of Combinations (Nc) is:

\[ Nc = \frac{C!}{n!(C-n)!} \]

Where:

\( Nc \) is the number of combinations
\( C \) is the total number of items
\( n \) is the number of items to choose
\( ! \) denotes factorial, which is the product of all positive integers up to that number

Number of Combinations (Nc): The number of ways to choose a subset of items from a larger set, without regard to the order of selection.
Significance: Used in probability and statistics to determine the number of possible outcomes in various scenarios, such as lottery draws, card games, and more.

Let's say the total number of items (C) is 5 and the number of items to choose (n) is 3. Using the formula:

\[ Nc = \frac{5!}{3!(5-3)!} = \frac{120}{6 \cdot 2} = 10 \]

So, the Number of Combinations (Nc) is 10.