Manuals/calci/COMBIN

COMBIN(Number,Numberchosen)

• $Number$ is the number of items.
• $NumberChosen$ 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 $n!=1*2*3*...*n$ & $r\leq n$.

• 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 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.

ZOS

• 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)
  • COMBIN(12.3,3) gives 220, though COMBIN(12.3d,3n) gives 238.5995. Here, the use of higher number types (like big number, decimal, etc.) different logic is triggered. In base plain numbers and Number objects, the numbers are truncated.

Combin

Examples

COMBIN(Number,NumberChosen)	Number	Numberchosen	RESULT
COMBIN(12,3)	12	3	220
COMBIN(4,4)	4	4	1
COMBIN(4,0)	4	0	1

a=34!C!3 
5984

COMBIN(PERMUT(34, 3n), 3) (For Big Integer) OR a=34n!P!3!C!3 = 7713313203904

Related Videos

COMBIN

See Also

• FACT
• PERMUT

References

Combination

• List of Main Z Functions

• Z3 home