COMBINA function

The COMBINA function in Excel is similar to the COMBIN function but with one key difference: COMBINA allows for repeated values in the combinations, whereas COMBIN assumes that each item is chosen only once. This makes COMBINA useful for situations where you can choose the same item more than once.

Syntax

=COMBINA(number, number_chosen)

Parameters

• number: The total number of items to choose from.
• number_chosen: The number of items you want to choose, including repeated selections.

Return Value

The function returns the number of possible combinations (subsets) that can be formed by selecting number_chosen items from number items, where repetition of items is allowed.

How It Works

The COMBINA function calculates combinations with repetition using the formula:

$$C(n, k) = \frac{(n+k-1)!}{k!(n-1)!}$$

Where:

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

Examples

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

   =COMBINA(5, 3)
   

   Result: 35
   (There are 35 possible ways to choose 3 items from 5, allowing for repeated choices.)

2. Choosing 2 from 7 with Repetition To find how many ways you can choose 2 items from a set of 7, allowing repetition:

   =COMBINA(7, 2)
   

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

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

   =COMBINA(5, 5)
   

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

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

   =COMBINA(4, 5)
   

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

Important Notes

• Repetition Allowed: Unlike the COMBIN function, COMBINA allows for repeated selections of the same item.
• Non-negative Integers: Both number and number_chosen must be non-negative integers. If either is negative, the function will return a #NUM! error.
• Factorial Calculation: The COMBINA function involves factorials, which can result in large numbers for higher values of number or number_chosen.

Use Cases

• Combinations with Replacement: Useful in scenarios where repetition is allowed, such as when selecting items from a group where you can pick the same item multiple times.
• Lotteries with Repetition: In some lottery systems, you may be able to pick the same number multiple times, and COMBINA can be used to calculate those outcomes.
• Grouping and Team Selection: When forming teams or groups with a possibility of repetition, the COMBINA function can help calculate how many possible combinations exist.

The COMBINA function is an essential tool in combinatorics for problems involving combinations where repetition is allowed.