Manuals/calci/COMBIN

COMBIN(n,r)

• $n$ is the number of items.
• $r$ is the number of items in each arrangement.

Description

• 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.
• Also if the order is not a matter, it is a Combination.
• If 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 $n!=1*2*3*...*n$ & $r\leq n$.
• This function will give Error Result when

1. The Failed to parse (syntax error): {\displaystyle n & r} are non numeric
2. The Failed to parse (syntax error): {\displaystyle n & r < 0} or $n<r$

• When we are giving the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n & r} values in decimals, it will automatically convert in to Integers.
• For e.g.
  • COMBIN(5.4,2)=10 is equivalent to COMBIN(5,2)
  • COMBIN(5,-2)=NAN, because $r$ is negative.

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