Difference between revisions of "Manuals/calci/COMBIN"

Revision as of 05:56, 18 March 2014

COMBIN(n,r)

This function gives the combination of $n$ objects.
i.e 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.
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 ${\binom {n}{r}}$ .
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 $n!=1*2*3*...*n$ & $r\leq n$ .

When we are giving the $n$ & $r$ 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 $r$ is negative.

Combination

The formula to calculate COMBINATION in ZOS is or
- $n$ is the number of items.
- $r$ is the number of items in each arrangement.

@@ Line 10: / Line 10: @@
 *If the order is a matter it is a Permutation.
 *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>.
 *This function will give Error Result when
 #The <math>n</math> & <math>r</math> are non numeric