Manuals/calci/COMBIN

COMBIN(Number,Numberchosen)

• $Number$ is the number of items.
• $Numberchosen$ is the number of items in each arrangement.

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

• This function will give Error Result when

1. The $n$ & $r$ are non numeric
2. The $n$ & $r<0$ or $n<r$

• 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.

ZOS Section

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)

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

See Also

• FACT
• PERMUT

References

Combination