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

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