COMBIN function

The COMBIN function in Excel is used to calculate the number of combinations (subsets) that can be made from a set of items, without considering the order of the items. It is commonly used in statistics, probability, and combinatorics.

Syntax

=COMBIN(number, number_chosen)

Parameters

• number: The total number of items to choose from.
• number_chosen: The number of items you want to choose from the total.

Return Value

The function returns the number of possible combinations (subsets) that can be formed by selecting number_chosen items from number items, where the order does not matter.

How It Works

The function calculates combinations using the combination formula:

$$C(n, k) = \frac{n!}{k! \cdot (n – k)!}$$

Where:

• n = total number of items (number).
• k = number of items chosen (number_chosen).
• ! denotes the factorial of a number.

Examples

1. Basic Combination Example To find how many ways you can choose 3 items from a set of 5:

   =COMBIN(5, 3)
   

   Result: 10
   (There are 10 possible ways to choose 3 items from 5.)

2. Choosing 2 from 7 Items To find how many ways you can choose 2 items from a set of 7:

   =COMBIN(7, 2)
   

   Result: 21
   (There are 21 possible ways to choose 2 items from 7.)

3. Choosing All Items To find how many ways you can choose all 5 items from a set of 5:

   =COMBIN(5, 5)
   

   Result: 1
   (There is only 1 way to choose all 5 items from 5.)

4. Choosing More Than Available Items If you try to choose more items than are available, Excel will return an error. For example:

   =COMBIN(4, 5)
   

   Result: #NUM!
   (You cannot choose 5 items from a set of 4.)

Important Notes

• Factorial Calculation: The COMBIN function internally calculates factorials, which can be quite large for higher values of number.
• Non-negative Integers: Both number and number_chosen must be non-negative integers. If either is negative, the function will return a #NUM! error.
• Order Does Not Matter: Unlike PERMUT (which calculates permutations where order does matter), COMBIN only counts combinations where the order of selection does not matter.

Use Cases

• Probability and Statistics: The COMBIN function is frequently used to calculate the number of possible outcomes in statistical experiments, where the order of selection is irrelevant.
• Lottery and Raffle Calculations: Useful for calculating the number of ways to choose lottery numbers or raffle tickets.
• Team Selection: For choosing a team of a certain size from a larger group, where the order of team members doesn’t matter.

This function provides a simple yet powerful way to calculate combinations and solve problems in combinatorics and probability.