# COMBIN Function in Excel

### Part 1: Introduce

Definition:
The COMBIN function in Microsoft Excel calculates the number of combinations for a given set of items.

Purpose:
The function determines the total possible number of groups for a given number of items.

Syntax & Arguments:

syntax
```COMBIN(number, number_chosen) ```
• Number: The total number of items.
• Number_chosen: The number of items in each combination.

Explain the Arguments in the function:

• Number: This is a required argument. It represents the total number of items you have.
• Number_chosen: Also a required argument. It signifies the number of items you want in each combination.

Return value:
The function returns the number of possible combinations.

Remarks:

• Numeric arguments are truncated to integers.
• If either argument is nonnumeric, COMBIN returns the #VALUE! Error value.
• If the number is less than 0, number_chosen is less than 0, or the number is less than number_chosen, COMBIN returns the #NUM! Error value.
• A combination is any set or subset of items, regardless of their internal order. This is different from permutations, where the order matters.

### Part 2: Examples

Example 1:

• Purpose of example: Determine the number of two-person teams from 8 candidates.
• Data sheet and formulas:
ABC
1
2Total Candidates8
3Team Size2
4Formula`=COMBIN(A2, A3)`
5Result28
• Explanation: From 8 candidates, there are 28 possible two-person teams.

Example 2:

• Purpose of example: Calculate the number of ways to choose 3 projects from a list of 10.
• Data sheet and formulas:
ABC
1
2Total Projects10
3Projects Chosen3
4Formula`=COMBIN(A2, A3)`
5Result120
• Explanation: From 10 projects, there are 120 ways to choose 3.

Example 3:

• Purpose of example: Determine the number of ways to select 4 products for a promotional bundle from a list of 12 products.
• Data sheet and formulas:
ABC
1
2Total Products12
3Products Chosen4
4Formula`=COMBIN(A2, A3)`
5Result495
• Explanation: From 12 products, there are 495 ways to select 4 for a promotional bundle.

Example 4:

• Purpose of example: Calculate the number of combinations to form 5-member committees from 15 employees.
• Data sheet and formulas:
ABC
1
2Total Employees15
3Committee Size5
4Formula`=COMBIN(A2, A3)`
5Result3,003
• Explanation: From a group of 15 employees, there are 3,003 ways to form a 5-member committee.

Example 5:

• Purpose of example: Determine the number of ways to select 6 items for a sample sale from a collection of 20 items.
• Data sheet and formulas:
ABC
1
2Total Items20
3Items Chosen6
4Formula`=COMBIN(A2, A3)`
5Result38,760
• Explanation: From a collection of 20 items, there are 38,760 ways to select 6 for a sample sale.

Example 6:

• Purpose of example: Calculate the number of ways to select 3 team leaders from 10 candidates, but only if there are more than 5 candidates.
• Data sheet and formulas:
ABCD
1
4Formula`=IF(A2>5, COMBIN(A2, A3), "N/A")`
5Result120
• Explanation: This example uses the `IF` function to check if there are more than 5 leaders. If accurate, it calculates the number of ways to select 3 leaders from 10 using the `COMBIN` function, resulting in 120 possible combinations. If not, it returns “N/A”.

Example 7:

• Purpose of example: Sum the combinations of choosing 2 products from 3 different product lines, each having other numbers of products.
• Data sheet and formulas:
ABCD
1Product Line
2Product Line 15`=COMBIN(B2, 2)`10
3Product Line 26`=COMBIN(B3, 2)`15
4Product Line 37`=COMBIN(B4, 2)`21
5Total Combinations`=SUM(C2:C4)`46
• Explanation: This example uses the `SUM` function to add up the combinations of choosing 2 products from each product line. The `COMBIN` function calculates the combinations for each product line separately.

Example 8:

• Purpose of illustration: Determine the number of ways to pair up items from two different lists, but only if the item from the first list exists in the second list using `VLOOKUP`.
• Data sheet and formulas:
ABCD
1List 1List 2
2Item 1AppleApple1
3Item 2BananaOrange0
4Item 3OrangeBanana0
5Formula`=COMBIN(IF(VLOOKUP(B2:C4, B2:C4, 1, FALSE), 1, 0), 2)`
6Result1
• Explanation: This example uses the `VLOOKUP` function to check if an item from List 1 exists in List 2. If it does, the `COMBIN` function calculates the number of ways to pair up the items.

Example 9:

• Purpose of illustration: Calculate the bonus for sales teams based on the possible team combinations they can form. Groups with more combinations get a higher bonus using the `IF` function.
• Data sheet and formulas:
ABCD
1Team Size
2Team A7`=IF(COMBIN(B2, 3)>10, "\$500", "\$300")`\$500
3Team B4`=IF(COMBIN(B3, 3)>10, "\$500", "\$300")`\$300
• Explanation: Teams that can form more than 10 combinations of 3 members get a bonus of \$500, while others earn \$300. The `COMBIN` function calculates the number of combinations and the `IF` function determines the premium.

Example 10:

• Purpose of illustration: Sum the number of ways to form pairs from three different departments using the `SUM` function.
• Data sheet and formulas:
ABCD
1Department
2Dept 16`=COMBIN(B2, 2)`15
3Dept 25`=COMBIN(B3, 2)`10
4Dept 37`=COMBIN(B4, 2)`21
5Total Pairs`=SUM(C2:C4)`46
• Explanation: The `COMBIN` function calculates the number of ways to form pairs from each department. The `SUM` function then adds these combinations to give the total number of pairs across all departments.

Example 11:

• Purpose of illustration: Determine the number of ways to select products for a promotional offer based on their ranking using the `RANK` function.
• Data sheet and formulas:
ABCDE
1ProductSalesRankingCombos
2Product 1Laptop500`=RANK(C2, C2:C4)``=COMBIN(D2, 2)`
3Product 2Phone600`=RANK(C3, C2:C4)``=COMBIN(D3, 2)`
4Product 3Headset300`=RANK(C4, C2:C4)``=COMBIN(D4, 2)`
• Explanation: Products are ranked based on their sales using the `RANK` function. The `COMBIN` function then calculates the number of ways to select products based on their ranking.

Example 12:

• Purpose of illustration: Calculate the number of ways to select team members based on their performance score using the `AVERAGE` function.
• Data sheet and formulas:
ABCDE
1MemberScoreAverageCombos
2Member 1John85`=AVERAGE(C2:C4)``=COMBIN(D2, 2)`
3Member 2Jane90`=AVERAGE(C2:C4)``=COMBIN(D3, 2)`
4Member 3Bob80`=AVERAGE(C2:C4)``=COMBIN(D4, 2)`
• Explanation: The performance score of each team member is averaged using the `AVERAGE` function. The `COMBIN` function then calculates the number of ways to select team members based on their average score.

### Part 3: Tips and tricks

1. Always ensure that the number chosen is less than or equal to the total number. Otherwise, you’ll get an error.
2. The COMBIN function only considers combinations, not permutations. If order matters, you might need a different function.
3. Use the COMBIN function in scenarios like team formations, project selections, or any situation where you need to find out the number of ways to choose items from a more extensive set.