COMBIN

Returns the number of combinations of a subset of items.

Syntax:

COMBIN(n, k)

n is the number of items in the set.k is the number of items to choose from the set. COMBIN returns the number of ways to choose these items. For example if there are 3 items A, B and C in a set, you can choose 2 items in 3 different ways, namely AB, AC and BC. COMBIN implements the formula:n!/(k!(n-k)!)

Example:

COMBIN(3, 2)

returns 3.

Application:

Scenario: A company is hosting a team-building event and wants to form groups of 3 employees for a problem-solving activity. There are 7 employees available to be in these groups. The order in which the employees are chosen for a group doesn't matter.

Question: How many different groups of 3 can be formed from the 7 employees?

To solve this, you can use the COMBIN function.

The formula would be: COMBIN(total_items, items_to_choose)

In this case:

total_items = 7 (the total number of employees)
items_to_choose = 3 (the size of each group)

The formula is: COMBIN(7, 3)

Table Representation:

	Total Employees	Group Size	COMBIN Function	Number of Possible Groups
	A	B	C	D
1	7	3	COMBIN(7, 3)	35

Explanation:

The COMBIN function calculates the result as 35. This means there are 35 unique combinations of 3-person groups that can be formed from the 7 employees.

If the employees are A, B, C, D, E, F, and G, some of the possible groups would be:

(A, B, C)
(A, B, D)
(A, B, E)
...and so on, until all 35 combinations are listed.

The group (A, B, C) is considered the same as (C, B, A) or (B, A, C) because the order of selection doesn't change the composition of the group. This is the key difference between combinations and permutations.