# COMBINA

The COMBINA function calculates the number of combinations with repetitions for a specified number of items. It is useful in situations where you want to determine the number of ways to combine a set of items, allowing for duplicates.

## Syntax

=COMBINA(`number`

, `number_chosen`

)

`number` | The total number of items available for combination | including duplicates. |

`number_chosen` | The number of items to be chosen for each combination. |

## About COMBINA

In the realm of permutations and combinations, the COMBINA function in Excel comes to the rescue when you need to figure out the number of ways to combine a specific set of items, allowing for repetition. This function proves its worth in numerous scenarios where you're dealing with a collection of items and need to ascertain the different possible groupings while taking into account the potential for duplicates among the items. It's particularly handy in fields such as probability, statistics, and combinatorics, offering a simple yet powerful tool for calculations involving combinations with repetitions. By providing the total number of items and the number of items to be chosen for each combination, you can obtain the number of unique combinations, considering items with duplicates. This can be immensely valuable when you're analyzing various potential outcomes arising from a pool of items, allowing you to effectively navigate the intricacies of diverse scenarios.

## Examples

Suppose you have a set of 3 different colors of balls and you want to select 2 balls at a time, with the possibility of choosing the same color multiple times. The COMBINA formula would be: =COMBINA(3, 2)

This will return the number of unique combinations of selecting 2 balls from the 3 colors, allowing for repetitions.

Consider a scenario where you need to create 4-digit PIN codes using digits 0-9, with the allowance for repeated digits. The COMBINA formula to determine the number of unique PIN codes would be: =COMBINA(10, 4)

This will provide the total number of distinct PIN codes that can be generated when allowing for repeated digits.

## Questions

**How does the COMBINA function differ from the COMBIN function?**

The primary distinction lies in the consideration of repetitions. The COMBINA function is used to calculate combinations allowing for repetition, while the COMBIN function computes combinations without repetition, also known as permutations. Therefore, if you need to account for duplicates among the items in your combinations, you would utilize the COMBINA function.

**In what scenarios can the COMBINA function be beneficial?**

The COMBINA function proves valuable in various scenarios where you want to determine the number of unique combinations of items, considering the possibility of duplicates. It can be particularly useful in probability and statistics, as well as in combinatorial mathematics, when analyzing situations involving the grouping and selection of items with the potential for repetition.

**What is the significance of allowing repetitions in combinations when using the COMBINA function?**

Allowing repetitions in combinations expands the scope of possible outcomes, especially relevant when dealing with scenarios where duplicate entries are permissible. For instance, in scenarios involving numbered or colored balls, or when generating PIN codes, allowing repetitions ensures thorough coverage of all possible combinations.

## Related functions

COMBIN