 # COMBIN

In this comprehensive guide, we will explore everything you need to know about the COMBIN function in Excel. The COMBIN function is a useful tool for calculating the number of possible combinations for a given set of items. This function is particularly helpful in statistics, probability, and combinatorics. By the end of this article, you will have a thorough understanding of the COMBIN function, its syntax, examples, tips and tricks, common mistakes, and related formulae.

## COMBIN Syntax

The syntax for the COMBIN function in Excel is as follows:

=COMBIN(number, number_chosen)

Where:

• number is the total number of items in the set. This argument must be a non-negative integer.
• number_chosen is the number of items to be chosen from the set. This argument must also be a non-negative integer.

The COMBIN function returns the number of combinations for a given set of items without considering the order of the items. The formula for calculating combinations is:

C(n, k) = n! / (k! * (n-k)!)

Where “n” is the total number of items, “k” is the number of items chosen, and “!” denotes the factorial of a number.

## COMBIN Examples

Let’s explore some examples of using the COMBIN function in Excel:

1. Example 1: You have a deck of 52 playing cards, and you want to know how many different 5-card poker hands can be dealt. To calculate this, you can use the COMBIN function as follows:
2. =COMBIN(52, 5)

This formula will return 2,598,960, which is the total number of possible 5-card poker hands.

1. Example 2: You are organizing a committee of 3 people from a group of 10 candidates. To find out how many different ways you can form the committee, use the COMBIN function:
2. =COMBIN(10, 3)

This formula will return 120, which is the total number of possible combinations for selecting 3 people from a group of 10.

1. Example 3: You have 8 different books and want to know how many ways you can choose 4 books to take on a trip. Use the COMBIN function to calculate the number of combinations:
2. =COMBIN(8, 4)

This formula will return 70, which is the total number of possible combinations for selecting 4 books from a set of 8.

## COMBIN Tips & Tricks

Here are some tips and tricks to help you make the most of the COMBIN function in Excel:

• Remember that the COMBIN function does not consider the order of the items. If you need to calculate permutations (where the order matters), use the PERMUT function instead.
• If you need to calculate combinations with repetitions allowed, use the COMBINA function.
• When working with large numbers, the COMBIN function may return a result in scientific notation. To display the result in a more readable format, you can change the cell format to “Number” and increase the number of decimal places if necessary.
• Be cautious when using non-integer values as arguments for the COMBIN function. Excel will truncate any decimal values to integers before performing the calculation.

## Common Mistakes When Using COMBIN

Here are some common mistakes to avoid when using the COMBIN function:

• Using negative numbers as arguments. Both the “number” and “number_chosen” arguments must be non-negative integers.
• Using the COMBIN function when the order of items matters. In such cases, use the PERMUT function instead.
• Forgetting that Excel truncates decimal values to integers. Ensure that you are using integer values as arguments for the COMBIN function.

## Why Isn’t My COMBIN Function Working?

If your COMBIN function is not working as expected, consider the following troubleshooting steps:

• Check that both the “number” and “number_chosen” arguments are non-negative integers.
• Ensure that you are using the correct function for your calculation. If the order of items matters, use the PERMUT function instead of COMBIN.
• Verify that your formula is entered correctly and that there are no typos or syntax errors.
• Make sure that your cell format is set to “Number” if the result is displayed in scientific notation.

## COMBIN: Related Formulae

Here are some related formulae that you may find useful when working with combinations and permutations in Excel:

1. PERMUT: Calculates the number of permutations for a given set of items. Use this function when the order of items matters.
2. =PERMUT(number, number_chosen)

3. COMBINA: Calculates the number of combinations with repetitions allowed for a given set of items.
4. =COMBINA(number, number_chosen)

5. FACT: Calculates the factorial of a given number.
6. =FACT(number)

7. FACTDOUBLE: Calculates the double factorial of a given number.
8. =FACTDOUBLE(number)

9. MULTINOMIAL: Calculates the multinomial coefficient for a given set of numbers.
10. =MULTINOMIAL(number1, [number2], …)

By mastering the COMBIN function and its related formulae, you can efficiently solve a wide range of problems involving combinations, permutations, and probability in Excel.

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