Difference between revisions of "Manuals/calci/COMBIN"
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*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>. | ||
*This function will give Error Result when | *This function will give Error Result when | ||
| − | #The <math>n & r</math> are non numeric | + | #The <math>n</math> & <math>r</math> are non numeric |
| − | #The <math>n & r < 0</math> or <math>n < r</math> | + | #The <math>n</math> & <math>r</math> < 0 </math> or <math>n < r</math> |
| − | *When we are giving the <math>n & r</math> values in decimals, it will automatically convert | + | *When we are giving the <math>n</math> & <math>r</math> values in decimals, it will automatically convert into Integers. |
*For e.g. | *For e.g. | ||
**COMBIN(5.4,2)=10 is equivalent to COMBIN(5,2) | **COMBIN(5.4,2)=10 is equivalent to COMBIN(5,2) | ||
Revision as of 23:37, 18 November 2013
COMBIN(n,r)
- is the number of items.
- is the number of items in each arrangement.
is the number of items.
is the number of items in each arrangement.Description
- This function gives the combination of objects.
- i.e. An arrangement of objects without any repetition, selected from 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.
- Also if the order is not a matter, it is a Combination.
- If 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 } & 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 </math> 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} & 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.
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 |