Difference between revisions of "Documentation/How Tos/Calc: COMBINA function"
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== COMBINA == | == COMBINA == | ||
− | Returns the number of | + | Returns the number of combinations of a subset of items. |
=== Syntax: === | === Syntax: === | ||
− | <tt>'''COMBINA( | + | <tt>'''COMBINA(n; k)'''</tt> |
− | : <tt>''' | + | : <tt>'''n'''</tt> is the number of items in the set. |
− | : <tt>''' | + | : <tt>'''k'''</tt> is the number of items to choose from the set. |
− | : <tt>'''COMBINA'''</tt> returns the number of ways to choose these items, where the order of choosing is | + | : <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: | ||
− | :: <tt>''' | + | :: <tt>'''(''n''+''k''-1)!/(''k''!(''n''-1)!)'''</tt> |
=== Example: === | === Example: === | ||
<tt>'''COMBINA(3,2)'''</tt> | <tt>'''COMBINA(3,2)'''</tt> | ||
: returns <tt>'''6'''</tt>. | : returns <tt>'''6'''</tt>. | ||
+ | |||
+ | <tt>'''COMBINA(3,3)'''</tt> | ||
+ | : returns <tt>'''10'''</tt>. | ||
=== See also: === | === See also: === | ||
− | '''[[Documentation/How_Tos/Calc: COMBIN function|COMBIN]]''' | + | '''[[Documentation/How_Tos/Calc: COMBIN function|COMBIN]]''', |
+ | '''[[Documentation/How_Tos/Calc: PERMUT function|PERMUT]]''', | ||
+ | '''[[Documentation/How_Tos/Calc: PERMUTATIONA function|PERMUTATIONA]]''' | ||
'''[[Documentation/How_Tos/Calc: Mathematical functions|Mathematical functions]]''' | '''[[Documentation/How_Tos/Calc: Mathematical functions|Mathematical functions]]''' |
Revision as of 12:52, 8 April 2008
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.