# COMBIN Function

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

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

The COMBIN Function is a 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.

**=COMBIN(number, number_chosen)**

The COMBIN function uses the following arguments:

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

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

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:

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.

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.

** **

- #VALUE! error – Occurs when either of the argument is non-numeric.
- #NUM! error – Occurs when the value of either argument is outside of its constraint.
- 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.

**Click here to download the sample Excel file**

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