# COMBINA Function

Calculate the number of combinations along with repetitions for a given number of items

Calculate the number of combinations along with repetitions for a given number of items

The COMBINA function is a Math and Trigonometry function. It will calculate for a given number of items the number of combinations along with repetitions. The function was introduced in MS Excel in 2013 and hence not available in earlier versions.

**=COMBINA(number, number_chosen)**

The COMBINA function uses the following arguments:

**Number**(required argument) – It should be either 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 must be greater than or equal to 0. Non-integer values are truncated.

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

Suppose we are given six numbers: 1, 2, 3, 4, 5, 6. Now let’s see how the COMBINA function calculates the number of combinations (with repetitions) for other numbers of objects taken from a set of 4.

For any six objects – a, b, c, d, e, f – there are 21 different combinations (with repetitions) of 2 objects. These are:

aa, ab, ac, ad, ae, af, bb, bc, bd, be, bf, cc, cd, ce, cf, dd, de, df, ee, ef, ff

The COMBINA function helps derive such combinations. It uses the formula (n+m-1) ÷ (n-1) where n is the number and m is the number_chosen. Remember the results of COMBINA above include repetitions.

Let’s see some interesting things about COMBINA. If you enter following arguments in a COMBINA function, the results will be:

COMBINA(0,0) is the only non-error output when n=0 yet this should be equal to COMBIN(-1,-1), which returns an error. It implies that the function includes an exception of n-m=0.

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), COMBINA will return the result 6; the combinations are aa, ab, ac, bb, bc, cc, whereas, COMBIN will return the result 3; the combinations are ab, ac, bc.
- The formula 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.

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

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