# COMBIN Function

Calculates the number of combinations without repetitions for a given number of items

## What is the COMBIN Function?

The COMBIN Function is an Excel Math and Trigonometry function. The function will calculate the number of combinations without repetitions for a given number of items. It was introduced in MS Excel 2000.

### Formula

=COMBIN(number, number_chosen)

The COMBIN function uses the following arguments:

1. Number (required argument) – The number should either be greater than or equal to 0. Also, it should be greater than or equal to the number_chosen. Non-integer values, if entered for this parameter, are truncated.
2. Number_chosen (required argument) – This is the number of items in each of the combinations. It must be greater than or equal to 0. Non-integer values are truncated.

### How to use the COMBIN Function in Excel?

To understand the uses of this function, let’s consider a few examples:

#### Example 1

Suppose we are given six numbers: 1, 2, 3, 4, 5, 6. Now let’s see how the COMBIN function calculates the number of combinations (without repetitions) for the other numbers of objects taken from a set of 4. For any six objects such as “a, b, c, d, e, f,” there are 15 different combinations (without repetitions) of two objects. These are:

ab, ac, ad, ae, af, bc, bd, be, bf, cd, ce, cf, de, df, ef

The COMBIN Function helps to derive such combinations as shown above. The number of combinations is as follows, where number = n and number_chosen = k: #### Example 2

Let’s now see how we can use this function in day-to-day life. Suppose there are 15 students and we wish to pair them into two-person teams. Using the COMBIN function, we can see the possible two-person teams that can be formed from 15 students. As seen above, 105 combinations without repetitions are possible.

### Difference between the COMBIN and COMBINA Functions

The COMBIN and COMBINA functions differ in the following ways:

• COMBIN does not count repetitions, whereas COMBINA does. For example, in a set of three objects – a, b, c – COMBIN would return the result 3; the combinations are ab, ac, bc. Whereas, COMBINA would return the result 6; the combinations are aa, ab, ac, bb, bc, cc.
• The formulas used by both functions are different.

### Things to remember about the COMBIN Function

1. #VALUE! error – Occurs when either of the arguments is non-numeric.
2. #NUM! error – Occurs when the value of either argument is outside of its constraint.
3. When we speak about a combination, it is any set or subset of items, regardless of its internal order. Combinations are separate from permutations, as the internal order is significant for permutations.