Difference between revisions of "Manuals/calci/COMBIN"
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==Description== | ==Description== | ||
*This function gives the combination of <math>n</math> objects. | *This function gives the combination of <math>n</math> objects. | ||
| − | *i.e | + | *i.e An arrangement of <math>r</math> objects without any repetition, selected from <math>n</math> different objects is called a combination of <math>n</math> objects taken <math>r</math> at a time. |
| − | * | + | *If the order is not a matter, it is a Combination. |
| − | *If order is a matter it is a Permutation. | + | *If the order is a matter it is a Permutation. |
*A combination is denoted by nCr or <math>\binom{n}{r}</math>. | *A combination is denoted by nCr or <math>\binom{n}{r}</math>. | ||
*A formula for the number of possible combinations of <math>r</math> objects from a set of <math>n</math> objects is <math>\binom{n}{r}=\frac{n!}{r!(n-r)!}</math> where <math>n!=1*2*3*...*n </math> & <math>r \le n</math>. | *A formula for the number of possible combinations of <math>r</math> objects from a set of <math>n</math> objects is <math>\binom{n}{r}=\frac{n!}{r!(n-r)!}</math> where <math>n!=1*2*3*...*n </math> & <math>r \le n</math>. | ||
Revision as of 07:44, 19 November 2013
COMBIN(n,r)
- 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} 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 r} is the number of items in each arrangement.
Description
- This function gives the combination of 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} objects.
- i.e An arrangement of 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} objects without any repetition, selected from 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} different objects is called a combination of 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} objects taken 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} at a time.
- 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 nCr 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 \binom{n}{r}} .
- A formula for the number of possible combinations of 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} objects from a set of 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} objects 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 \binom{n}{r}=\frac{n!}{r!(n-r)!}} where 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!=1*2*3*...*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 r} values in decimals, it will automatically convert into Integers.
- For e.g.
- COMBIN(5.4,2)=10 is equivalent to COMBIN(5,2)
- COMBIN(5,-2)=NAN, because 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} is negative.
& 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 automatically convert into Integers.Examples
| COMBIN(n,r) | n | r | RESULT |
|---|---|---|---|
| COMBIN(12,3) | 12 | 3 | 220 |
| COMBIN(4,4) | 4 | 4 | 1 |
| COMBIN(4,0) | 4 | 0 | 1 |