# Documentation/Calc Functions/COMBIN

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COMBIN

Mathematical

## Summary:

Calculates the number of combinations when choosing a subset of k objects from a pool of n objects (without repetition).

## Syntax:

COMBIN(Number1; Number2)

## Returns:

Returns a positive integer that is the number of combinations (without repetition) for the given arguments.

## Arguments:

Number1 is a non-negative integer, or a reference to a cell containing that number, that is the number of objects in the pool.

Number2 is a non-negative integer, or a reference to a cell containing that number, that is the number of objects to be chosen from the pool.

• If either Number1 or Number2 is non-numeric, then COMBIN reports a #VALUE! error.
• If either Number1 or Number2 is a non-integer value, then COMBIN converts it to an integer by taking its floor value.
• If either Number1 or Number2 is less than 0, then COMBIN reports an invalid argument error (Err:502).
• If Number1 < Number2, then COMBIN reports an invalid argument error (Err:502).

• The formula specifying the number of possible combinations if selecting k items from a collection of n items (with no repetition and when order does not matter), with kn, is as follows:

$\displaystyle{ \text{COMBIN}(n,k) ~=~\frac{n!}{k!(n-k)!} }$

• The resulting number of combinations is often referred to as "n choose k" and occurs in several areas of mathematics, including as a binomial coefficient. It also has several notations, including $\displaystyle{ C(n,k) }$, $\displaystyle{ _{n}C_{k} }$, and $\displaystyle{ \binom{n}{k} }$.

## Examples:

Formula Description Returns
=COMBIN(3; 2) From a pool of 3 items, 2 can be chosen in 3 ways. 3
=COMBIN(7.6;3.3) COMBIN truncates both arguments, to 7 and 3 respectively. From a pool of 7 items, 3 can be chosen in 35 ways. 35
=COMBIN(D1; D2) where cells D1 and D2 contain the values 52 and 13 respectively. From a standard deck of 52 playing cards, there are 635013559600 ways of dealing a bridge hand comprising 13 cards. 635013559600

COMBIN