Difference between revisions of "Manuals/calci/COMBIN"

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<div style="font-size:30px">'''COMBIN(Number,Numberchosen)'''</div><br/>
  
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Syntax
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*<math>Number</math> is the number of items.
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*<math>NumberChosen</math> is the  number of items in each arrangement.
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**COMBIN() returns the number of combinations for a given number of objects.
  
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==Description==
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*This function gives the combination of the given number of objects.
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*Let Number be "n" and Number chosen be "r".
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*So the Combinations is an arrangement of <math>r</math> objects without any repetition, selected from <math>n</math> different objects is called a combination of <math>n</math> objects taken <math>r</math> at a time.
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*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.
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*If the order is not a matter, it is a Combination.
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*If the order is a matter it is a Permutation.
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*A combination is denoted by <math>^nC_r</math> or <math>\binom{n}{r}</math> or <math>C(n,r)</math>.
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*A formula for the number of possible combinations of <math>r</math> objects from a set of <math>n</math> objects is:
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<math>\binom{n}{r}=\frac{n!}{r!(n-r)!}</math>
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where <math>n!=1*2*3*...*n </math> & <math>r \le n</math>.
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*This function will give Error Result when
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#The <math>n</math> & <math>r</math> are non numeric
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#The <math>n</math> & <math>r < 0 </math> or <math>n < r</math>
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*When we are giving the <math>n</math> & <math>r</math> values in decimals, it will truncated into Integers.
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*For e.g.
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**COMBIN(5.4,2)=10 is equivalent to COMBIN(5,2)
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**COMBIN(5,-2)=#N/A (NUMBERCHOSEN > 0), because <math>r</math> is negative.
  
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Remarks
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==ZOS==
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*The syntax is to calculate COMBIN in ZOS is <math>COMBIN(Number,NumberChosen)</math>
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**<math>Number</math> is the number of items.
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**<math>NumberChosen</math> is the  number of items in each arrangement.
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**For e.g.,COMBIN(20..23,6..7)
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**COMBIN(4,2)*COMBIN(10,5)
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**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.
  
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{{#ev:youtube|cQXPq6y8bOw|280|center|Combin}}
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Examples
 
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<div id="8SpaceContent" align="left"><div class="ZEditBox" align="justify">'''<font face="Times New Roman">''''''''''''<font size="6"> </font>''' '''''''''</font>'''</div></div>
 
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<font size="5">Description</font>
 
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<div id="10SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">'''<font face="Times New Roman"> <font size="6">COMBIN</font> </font>'''</div></div>
 
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<div id="3SpaceContent" class="zcontent" align="left"><br /><div id="7Space" class="gamizbox" title="7Space"><div id="7SpaceHeader" class="zheaderstyle" title="Double-click to start and stop editing the header."><center></center></div><div id="7SpaceRollup" title="Double-click to rolldown" align="left"><span><span id="7SpaceRollupContent" align="center"></span></span></div><div id="7SpaceCover"><div id="7SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">
 
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'''COMBIN''' (N, M)
 
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'''Where N''' is the no. of items and M is the no. of items in the arrangement.
 
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<div id="13SpaceContent" class="zcontent" align="left"><br /><br /><div id="1Space" class="gamizbox" title="1Space"><div id="1SpaceHeader" class="zheaderstyle" title="Double-click to start and stop editing the header."><center></center></div><div id="1SpaceRollup" title="Double-click to rolldown" align="left"><span><span id="1SpaceRollupContent" align="center"></span></span></div><div id="1SpaceCover"><div id="1SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">
 
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·          COMBIN calculates an error value when the argument is nonnumeric.
 
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·          The number of combinations is as follows, where N(no. of items) = n and M(no. of items in the arrangement) = k:
 
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Formula:-
 
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It calculates the number of combinations for the known items.
 
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==Examples==
 
{| id="TABLE3" class="SpreadSheet blue"
 
{| id="TABLE3" class="SpreadSheet blue"
 
|- class="even"
 
|- class="even"
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| class="  " |
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| COMBIN(Number,NumberChosen)
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<div id="6Space_Copy" title="Click and Drag over to AutoFill other cells."></div>
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! Number
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| Column1
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! Numberchosen
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| class="  " | Column2
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! RESULT
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| class="  " | Column3
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|-
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| class="  " | Column4
 
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|- class="odd"
 
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| class=" " | Row1
 
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| class=" " | 35
 
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| class="sshl_f " | 8
 
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| class="sshl_f" |
 
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| class="sshl_f" |
 
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|- class="even"
 
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| class="  " | Row2
 
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| class="sshl_f" | 23535820
 
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| class="sshl_f" |
 
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| class="sshl_f" |
 
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| class="sshl_f" |
 
 
|- class="odd"
 
|- class="odd"
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| Row3
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|COMBIN(12,3)
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| class="sshl_f SelectTD SelectTD" |
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|12
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<div id="6Space_Handle" title="Click and Drag to resize CALCI Column/Row/Cell. It is EZ!"></div><div id="6Space_Copy" title="Click and Drag over to AutoFill other cells."></div>
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|3
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| class="sshl_f" |
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|220
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| class="sshl_f" |
 
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| class="sshl_f" |
 
 
|- class="even"
 
|- class="even"
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| Row4
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|COMBIN(4,4)
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| class="sshl_f" |
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|4
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| class="sshl_f" |
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|4
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| class="sshl_f" |
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|1
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| class="sshl_f" |
 
 
|- class="odd"
 
|- class="odd"
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| class=" " | Row5
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|COMBIN(4,0)
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| class="sshl_f" |
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|4                                     
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| class="sshl_f" |
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|0
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| class="sshl_f" |
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|1
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| class="sshl_f" |
 
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|- class="even"
 
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| Row6
 
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| class="sshl_f" |
 
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| class="sshl_f" |
 
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| class="sshl_f" |
 
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| class="sshl_f" |
 
 
|}
 
|}
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a=34!C!3
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5984
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COMBIN(PERMUT(34, 3n), 3) (For Big Integer) OR a=34n!P!3!C!3 = 7713313203904
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==Related Videos==
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{{#ev:youtube|Bzuj8ItKT5w|280|center|COMBIN}}
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==See Also==
  
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<div align="left">[[Image:calci1.gif]]</div></div>
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*[[Manuals/calci/FACT | FACT]]
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*[[Manuals/calci/PERMUT | PERMUT ]]
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<div id="9SpaceContent" class="zcontent" align="left"> 
 
  
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Lets see an example in (Column1, Row 1 and Column 2, Row2)
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==References==
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[http://en.wikipedia.org/wiki/Combination  Combination]
  
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COMBIN (A, B)
 
  
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COMBIN (C1R1, C2R1)''''''
 
  
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That is COMBIN (35, 8) is 23535820
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*[[Z_API_Functions | List of Main Z Functions]]
  
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</div></div>
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*[[ Z3 |  Z3 home ]]
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</div></div></div></div></div></div></div>
 

Latest revision as of 04:18, 24 February 2022

COMBIN(Number,Numberchosen)


  • is the number of items.
  • 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 objects without any repetition, selected from different objects is called a combination of objects taken 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 or or .
  • A formula for the number of possible combinations of objects from a set of objects is:

where & .

  • This function will give Error Result when
  1. The & are non numeric
  2. The & or
  • When we are giving the & 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 is negative.

ZOS

  • The syntax is to calculate COMBIN in ZOS is
    • is the number of items.
    • 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

References

Combination


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