Difference between revisions of "Manuals/calci/COMBIN"

Revision as of 03:44, 9 April 2014

COMBIN(Number,Numberchosen)

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 $n!=1*2*3*...*n$ & $r\leq n$ .

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 syntax is to calculate COMBIN in ZOS is COMBIN(Number,Numberchosen)
- $Number$ is the number of items.
- $Numberchosen$ is the number of items in each arrangement.
- For e.g.,COMBIN(20..23,6..7)
- COMBIN(4,2)*COMBIN(10,5)

@@ Line 11: / Line 11: @@
 *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 <math>\binom{n}{r}</math> or <math>C(n,r)</math>.
+*A combination is denoted by <math>^nC_r</math> or <math>\binom{n}{r}</math> or <math>C(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>