Manuals/calci/COMBIN

COMBIN(Number,Numberchosen)

$Number$ is the number of items.
is the number of items in each arrangement.
- COMBIN() returns the number of combinations for a given number of objects.

Description

This function gives the combination of the given number of objects.
Let Number be "n" and Number chosen be "r".
So the Combinations is an arrangement of $r$ objects without any repetition, selected from $n$ different objects is called a combination of $n$ objects taken $r$ at a time.
For example consider three colors, like Blue,Yellow,Pink.There are three combinations of two can be drawn from the set:Blue and Yellow,Blue and Pink,or Yellow and Pink.
If the order is not a matter, it is a Combination.
If the order is a matter it is a Permutation.
A combination is denoted by $^{n}C_{r}$ or ${\binom {n}{r}}$ or $C(n,r)$ .
A formula for the number of possible combinations of $r$ objects from a set of $n$ objects is:

 ${\binom {n}{r}}={\frac {n!}{r!(n-r)!}}$

where $n!=1*2*3*...*n$ & Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r \le n} .

This function will give Error Result when

The Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} & Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} are non numeric
The Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} & Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r < 0 } or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n < r}

When we are giving the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} & Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} values in decimals, it will truncated into Integers.
For e.g.
- COMBIN(5.4,2)=10 is equivalent to COMBIN(5,2)
- COMBIN(5,-2)=#N/A (NUMBERCHOSEN > 0), because $r$ is negative.

ZOS

The syntax is to calculate COMBIN in ZOS is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle COMBIN(Number,NumberChosen)}
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Number} is the number of items.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle NumberChosen} is the number of items in each arrangement.
- For e.g.,COMBIN(20..23,6..7)
- COMBIN(4,2)*COMBIN(10,5)
- COMBIN(12.3,3) gives 220, though COMBIN(12.3d,3n) gives 238.5995. Here, the use of higher number types (like big number, decimal, etc.) different logic is triggered. In base plain numbers and Number objects, the numbers are truncated.