### 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:**

A | B | C | |
---|---|---|---|

1 | |||

2 | Total Candidates | 8 | |

3 | Team Size | 2 | |

4 | Formula | `=COMBIN(A2, A3)` | |

5 | Result | 28 |

**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:**

A | B | C | |
---|---|---|---|

1 | |||

2 | Total Projects | 10 | |

3 | Projects Chosen | 3 | |

4 | Formula | `=COMBIN(A2, A3)` | |

5 | Result | 120 |

**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:**

A | B | C | |
---|---|---|---|

1 | |||

2 | Total Products | 12 | |

3 | Products Chosen | 4 | |

4 | Formula | `=COMBIN(A2, A3)` | |

5 | Result | 495 |

**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:**

A | B | C | |
---|---|---|---|

1 | |||

2 | Total Employees | 15 | |

3 | Committee Size | 5 | |

4 | Formula | `=COMBIN(A2, A3)` | |

5 | Result | 3,003 |

**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:**

A | B | C | |
---|---|---|---|

1 | |||

2 | Total Items | 20 | |

3 | Items Chosen | 6 | |

4 | Formula | `=COMBIN(A2, A3)` | |

5 | Result | 38,760 |

**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:**

A | B | C | D | |
---|---|---|---|---|

1 | ||||

2 | Total Leaders | 10 | ||

3 | Leaders Chosen | 3 | ||

4 | Formula | `=IF(A2>5, COMBIN(A2, A3), "N/A")` | ||

5 | Result | 120 |

**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:**

A | B | C | D | |
---|---|---|---|---|

1 | Product Line | |||

2 | Product Line 1 | 5 | `=COMBIN(B2, 2)` | 10 |

3 | Product Line 2 | 6 | `=COMBIN(B3, 2)` | 15 |

4 | Product Line 3 | 7 | `=COMBIN(B4, 2)` | 21 |

5 | Total 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:**

A | B | C | D | |
---|---|---|---|---|

1 | List 1 | List 2 | ||

2 | Item 1 | Apple | Apple | 1 |

3 | Item 2 | Banana | Orange | 0 |

4 | Item 3 | Orange | Banana | 0 |

5 | Formula | `=COMBIN(IF(VLOOKUP(B2:C4, B2:C4, 1, FALSE), 1, 0), 2)` | ||

6 | Result | 1 |

**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:**

A | B | C | D | |
---|---|---|---|---|

1 | Team Size | |||

2 | Team A | 7 | `=IF(COMBIN(B2, 3)>10, "$500", "$300")` | $500 |

3 | Team B | 4 | `=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:**

A | B | C | D | |
---|---|---|---|---|

1 | Department | |||

2 | Dept 1 | 6 | `=COMBIN(B2, 2)` | 15 |

3 | Dept 2 | 5 | `=COMBIN(B3, 2)` | 10 |

4 | Dept 3 | 7 | `=COMBIN(B4, 2)` | 21 |

5 | Total 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:**

A | B | C | D | E | |
---|---|---|---|---|---|

1 | Product | Sales | Ranking | Combos | |

2 | Product 1 | Laptop | 500 | `=RANK(C2, C2:C4)` | `=COMBIN(D2, 2)` |

3 | Product 2 | Phone | 600 | `=RANK(C3, C2:C4)` | `=COMBIN(D3, 2)` |

4 | Product 3 | Headset | 300 | `=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:**

A | B | C | D | E | |
---|---|---|---|---|---|

1 | Member | Score | Average | Combos | |

2 | Member 1 | John | 85 | `=AVERAGE(C2:C4)` | `=COMBIN(D2, 2)` |

3 | Member 2 | Jane | 90 | `=AVERAGE(C2:C4)` | `=COMBIN(D3, 2)` |

4 | Member 3 | Bob | 80 | `=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

- Always ensure that the number chosen is less than or equal to the total number. Otherwise, you’ll get an error.
- The COMBIN function only considers combinations, not permutations. If order matters, you might need a different function.
- 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.