Documentation/Calc Functions/COMBIN

Function name:
COMBIN

Category:
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).

Additional details:
$$\text{COMBIN}(n,k) ~=~\frac{n!}{k!(n-k)!}$$
 * 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 k ≤ n, is as follows:


 * 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 $$C(n,k)$$, $$_{n}C_{k}$$, and $$\binom{n}{k}$$.


 * For more information, visit Wikipedia’s Combination page.

Related LibreOffice functions:
COMBINA

PERMUT

PERMUTATIONA

ODF standard:
Section 6.16.16, part 2

Equivalent Excel functions:
COMBIN