Documentation/Calc Functions/COMBIN
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Function name:
COMBIN
Category:
Mathematical
Summary:
Calculates the number of combinations when choosing a subset of k objects from a pool of n objects. with no repetition.
Syntax:
COMBIN(Number1; Number2)
Returns:
Returns a positive integer that is the number of combinations with no 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:
- 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:[math]\displaystyle{ \text{COMBIN}(n,k) ~=~\frac{n!}{k!(n-k)!} }[/math]
- 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 [math]\displaystyle{ C(n,k) }[/math], [math]\displaystyle{ _{n}C_{k} }[/math], and [math]\displaystyle{ \binom{n}{k} }[/math].
- For more information, visit Wikipedia’s Combination page.
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) | Truncate 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 |
Related LibreOffice functions:
ODF standard:
Related (or similar) Excel functions:
COMBIN