Difference between revisions of "Documentation/How Tos/Calc: COMBINA function"

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{{DISPLAYTITLE:COMBINA function}}
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== COMBINA ==
 
== COMBINA ==
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Returns the number of ordered combinations of a subset of items.
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Returns the number of combinations of a subset of items.
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=== Syntax: ===
 
=== Syntax: ===
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<tt>'''COMBINA(setsize; subsetsize)'''</tt>
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<tt>'''COMBINA(n; k)'''</tt>
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: <tt>'''setsize'''</tt> is the number of items in the set.
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: <tt>'''n'''</tt> is the number of items in the set.
  
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: <tt>'''subsetsize'''</tt> is the number of items to choose from the set.
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: <tt>'''k'''</tt> is the number of items to choose from the set.
  
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: <tt>'''COMBINA'''</tt> returns the number of ways to choose these items, where the order of choosing is important. For example if there are 3 items A, B and C in a set, you can choose 2 items in 6 different ways, namely AB, BA, AC, CA, BC and CB.
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: <tt>'''COMBINA'''</tt> returns the number of unique ways to choose these items, where the order of choosing is irrelevant, and repetition of items is allowed. For example if there are 3 items A, B and C in a set, you can choose 2 items in 6 different ways, namely AA, AB, AC, BB, BC and CC; you can choose 3 items in 10 different ways, namely AAA, AAB, AAC, ABB, ABC, ACC, BBB, BBC, BCC, CCC.
  
 
: <tt>'''COMBINA'''</tt> implements the formula:
 
: <tt>'''COMBINA'''</tt> implements the formula:
  
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:: <tt>'''setsize!/(setsize-subsetsize)!'''</tt>
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:: <tt>'''(''n''+''k''-1)!/(''k''!(''n''-1)!)'''</tt>
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=== Example: ===
 
=== Example: ===
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: returns <tt>'''6'''</tt>.
 
: returns <tt>'''6'''</tt>.
  
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<tt>'''COMBINA(3,3)'''</tt>
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: returns <tt>'''10'''</tt>.
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{{SeeAlso|EN|
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* [[Documentation/How_Tos/Calc: COMBIN function|COMBIN]]
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* [[Documentation/How_Tos/Calc: PERMUT function|PERMUT]]
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* [[Documentation/How_Tos/Calc: PERMUTATIONA function|PERMUTATIONA]]
  
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=== See also: ===
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* [[Documentation/How_Tos/Calc: Mathematical functions|Mathematical functions]]
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'''[[Documentation/How_Tos/Calc: COMBIN function|COMBIN]]'''
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'''[[Documentation/How_Tos/Calc: Mathematical functions|Mathematical functions]]'''
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* [[Documentation/How_Tos/Calc: Functions listed alphabetically|Functions listed alphabetically]]
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* [[Documentation/How_Tos/Calc: Functions listed by category|Functions listed by category]]}}
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[[Category: Documentation/Reference/Calc/Mathematical functions]]

Latest revision as of 15:08, 31 January 2024

COMBINA

Returns the number of combinations of a subset of items.

Syntax:

COMBINA(n; k)

n is the number of items in the set.
k is the number of items to choose from the set.
COMBINA returns the number of unique ways to choose these items, where the order of choosing is irrelevant, and repetition of items is allowed. For example if there are 3 items A, B and C in a set, you can choose 2 items in 6 different ways, namely AA, AB, AC, BB, BC and CC; you can choose 3 items in 10 different ways, namely AAA, AAB, AAC, ABB, ABC, ACC, BBB, BBC, BCC, CCC.
COMBINA implements the formula:
(n+k-1)!/(k!(n-1)!)

Example:

COMBINA(3,2)

returns 6.

COMBINA(3,3)

returns 10.


See Also
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