This guide covers everything you need to know about the Google Sheets COMBIN function, including its definition, syntax, use cases, and how to use it.

## What is the COMBIN Function? How Does It Work?

The COMBIN function in Google Sheets is a mathematical formula that returns the number of combinations possible when choosing a specific number of items from a larger pool of objects. It is an implementation of the standard combinatorics function, usually denoted as nCk, or “n choose k”.

This function is based on the principles of combination in mathematics, which is a way of selecting items from a collection where the order of selection does not matter. It is often used in probability theory and statistics for calculating the number of possible combinations of a set of objects.

In Google Sheets, the COMBIN function is used to automate this calculation process. For instance, if you have a pool of 8 items (n) and want to know how many ways you can choose 3 items (k) from this pool, the COMBIN function will return the total number of possible combinations.

The COMBIN function works by dividing the factorial of the total number of objects (n), by the product of the factorial of the number of objects to choose (k) and the factorial of the difference between the total number of objects and the number of objects to choose (n-k). It’s equivalent to the mathematical expression FACT(n)/(FACT(k)*FACT(n-k)).

To provide a practical example, the function COMBIN(4,2) will return the value of 6. This means that if you had a set of 4 objects, there are 6 different ways you could select 2 objects from that set.

This function can be incredibly useful in various fields, including business analytics, project management, and more. It enables users to automatically calculate complex combinations, thereby saving valuable time and reducing the potential for human error.

## COMBIN Syntax

The syntax and arguments for the COMBIN function are as follows:

**COMBIN(n, k)**

In this syntax:

**‘n’**represents the size of the pool of objects to choose from. This argument should be a positive integer.**‘k’**represents the number of objects to choose from the pool. This argument should also be a positive integer and cannot exceed ‘n’.

Here are some important usage notes related to the syntax and arguments of the COMBIN function:

- Both ‘n’ and ‘k’ should be non-negative integers. If not, Google Sheets will return an error.
- The COMBIN function will return an error if ‘k’ is greater than ‘n’ because it is impossible to choose more objects than the total number available in the pool.
- In the context of the COMBIN function, ‘n’ and ‘k’ are typically notated as nCk and read as “n choose k”. This is the standard notation in combinatorics.
- The COMBIN function is equivalent to the formula FACT(n)/(FACT(k)*FACT(n-k)), where FACT denotes the factorial of a number.
- If either ‘n’ or ‘k’ is not a whole number, Google Sheets will round it down to the nearest whole number before performing the calculation.
- The COMBIN function can handle large numbers, but it may return a #NUM! error if the result exceeds the maximum limit that Google Sheets can handle.
- The COMBIN function is not case-sensitive, so you can use either uppercase or lowercase letters (or a combination of both) when entering it.

## Examples of How to Use the COMBIN Function

Here are some practical examples of how you can use the COMBIN function in Google Sheets.

### Example #1: Calculating Combinations in a Lottery Draw

Suppose you’re playing a lottery game where you have to choose 6 numbers out of a possible 49. You want to know how many different combinations of 6 numbers can be drawn. This is where the COMBIN function can be handy.

The formula you’ll use in Google Sheets is =COMBIN(49,6). This will return 13,983,816, which is the total number of combinations of 6 numbers that can be drawn from a pool of 49.

### Example #2: Determining Possible Team Combinations

Let’s say you’re a coach and have 11 players on your soccer team. You’re trying to figure out how many different combinations of 5 players can be on the field at a time.

In this case, you will input =COMBIN(11,5) into a cell in Google Sheets. The result will be 462, indicating there are 462 different combinations of 5 players that can be chosen from a team of 11.

### Example #3: Figuring Out Possible Investment Combinations

Imagine you’re an investor with 7 different stocks to choose from, and you want to create a portfolio containing 3 different stocks. You want to know how many different portfolios you could potentially create.

You would use the COMBIN function by inputting =COMBIN(7,3) into a cell. Google Sheets will return 35, indicating there are 35 different combinations of 3 stocks you can choose from a total of 7.

## COMBIN: Common Mistakes & Problems

When using the COMBIN function in Google Sheets, there are several common mistakes and problems that you may encounter.

**Incorrect Argument Order**: The COMBIN function requires two arguments: the total number of items and the number of items to choose. Mixing up the order of these arguments will result in an error. The correct syntax is COMBIN(n, k), where n is the total number of items and k is the number of items to choose.**Using Non-Integer Values**: The COMBIN function only accepts integer values. If you use non-integer values as arguments, Google Sheets will round them down to the nearest integer. This might not give you the result you were expecting.**Using Negative Values**: The COMBIN function doesn’t accept negative values. If you use a negative value as an argument, Google Sheets will return an error.**Using Large Values**: The COMBIN function can handle large values, but be aware that using very large values can cause Google Sheets to slow down or even crash. If you need to calculate combinations for very large numbers, consider using a different method or tool.**Not Enough Items to Choose From**: If you attempt to choose more items than are available (i.e., your k value is larger than your n value), Google Sheets will return an error. Ensure your k value is always less than or equal to your n value.

## Why Is COMBIN Not Working? Troubleshooting Common Errors

If you are using the COMBIN function in Google Sheets and it’s not working, there could be several reasons behind it. This section will focus on common errors, their causes, and solutions to help you troubleshoot the issues.

### #VALUE! Error

**Cause**: This error occurs if either of the arguments in the COMBIN function (number, number_chosen) is non-numeric or if the number_chosen value is greater than the number value.

**Solution**: Make sure that both arguments are numeric and that the number_chosen value is less than or equal to the number value.

### #NUM! Error

**Cause**: This error appears when either of the arguments in the COMBIN function is less than 0 or if the number_chosen is greater than the number.

**Solution**: Ensure that both the number and number_chosen values are greater than or equal to 0 and that the number_chosen is not greater than the number.

### #N/A Error

**Cause**: This error happens when the COMBIN function does not have enough data to calculate a result. It could be that one or both of the arguments are missing.

**Solution**: Ensure that both arguments, number and number_chosen, are present in the function.

### Circular Reference Error

**Cause**: This error occurs when a cell refers to itself, either directly or indirectly, creating a loop.

**Solution**: Check the formula for any possible self-references and modify the formula to prevent any circular references.

### Array Arguments Error

**Cause**: This error occurs if the number or number_chosen arguments in the COMBIN function are array values. The COMBIN function in Google Sheets does not support array arguments.

**Solution**: Make sure the number and number_chosen arguments are single values, not array values.

By understanding these common errors, their causes, and solutions, you can troubleshoot and resolve any issues you may have with the COMBIN function in Google Sheets.

## Using COMBIN With Other Google Sheets Functions

Combining the COMBIN function with other Google Sheets functions can yield some powerful results. Here are a few ways you can use COMBIN in conjunction with other functions:

### With SUM

**Usage**: You can use the SUM function with COMBIN to add together the results of several different combinations. For example, you might want to calculate the total number of possible combinations for different sets of numbers.

**Example**: Suppose you have three sets of numbers in cells A1, B1, and C1, and you want to find the total number of possible combinations of two numbers from each set. You could use the formula =SUM(COMBIN(A1,2), COMBIN(B1,2), COMBIN(C1,2)).

### With AVERAGE

**Usage**: Use the AVERAGE function with COMBIN to find the average number of combinations for a set of numbers. This could be useful for statistical analysis.

**Example**: If you have a range of numbers in cells A1 through A5, and you want to find the average number of combinations of two numbers from these sets, you could use the formula =AVERAGE(COMBIN(A1,2), COMBIN(A2,2), COMBIN(A3,2), COMBIN(A4,2), COMBIN(A5,2)).

### With IF

**Usage**: You can use the IF function with COMBIN to calculate based on a condition. For instance, you might want to calculate combinations only if a certain condition is met.

**Example**: Suppose you have a set of numbers in cells A1 through A5 and want to find the number of combinations of two numbers only if the number is greater than 5. You could use the formula =IF(A1>5, COMBIN(A1,2), 0).

### With ARRAYFORMULA

**Usage**: Use the ARRAYFORMULA function with COMBIN to apply the COMBIN function to an entire range of cells at once.

**Example**: If you have a range of numbers in cells A1 through A5 and you want to find the number of combinations of two numbers for each of these, you could use the formula =ARRAYFORMULA(COMBIN(A1:A5,2)).

For more details on the COMBIN function, check out the official documentation at the Google Docs Editors Help Center.