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 $Number$ objects.
• i.e An arrangement of $Numberchosen$ objects without any repetition, selected from $Number$ different objects is called a combination of $Number$ objects taken $Numberchosen$ at a time.
• If the order is not a matter, it is a Combination.
• If the order is a matter it is a Permutation.
• Let Number be "n" and Number chosen be "r".
• 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 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!=1*2*3*...*n } & 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 r \le n} .

• This function will give Error Result when

1. 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} & 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 r} are non numeric
2. 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} & 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 r < 0 } or 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}

• When we are giving the $n$ & 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 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 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 r} is negative.

ZOS Section

Combination

• The syntax is to calculate COMBIN in ZOS is COMBIN(Number,Numberchosen)
  • 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 Number} is the number of items.
  • 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 Numberchosen} is the number of items in each arrangement.
  • For e.g.,COMBIN(20..23,6..7)

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