Difference between revisions of "Manuals/calci/COMBIN"

Latest revision as of 03:18, 24 February 2022

COMBIN(Number,Numberchosen)

$Number$ 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 $r$ objects without any repetition, selected from $n$ different objects is called a combination of $n$ objects taken $r$ 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 $^{n}C_{r}$ or ${\binom {n}{r}}$ or $C(n,r)$ .
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

The $n$ & $r$ are non numeric
The $n$ & $r<0$ or $n<r$

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

ZOS

The syntax is to calculate COMBIN in ZOS is
- $Number$ is the number of items.
- $NumberChosen$ 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

References

Combination

List of Main Z Functions

Z3 home

@@ Line 1: / Line 1: @@
-<div style="font-size:30px">'''COMBIN(n,r)'''</div><br/>
+<div style="font-size:30px">'''COMBIN(Number,Numberchosen)'''</div><br/>
-*'N' is the number of items.
+*<math>Number</math> is the number of items.
-*'R' is the  number of items in each arrangement.
+*<math>NumberChosen</math> 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 N objects.
+*This function gives the combination of the given number of objects.
-i.e.An arrangement of R objects without any repetition,
+*Let Number be "n" and Number chosen be "r".
-selected from N different objects is called a combination of N objects taken  R at a time.
+*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.
-Also if the order doesn't a matter, it is a combination.
+*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 order is the matter it is a permutation.
+*If the order is not a matter, it is a Combination.
-A combination is dnoted by ncr or(n  r).
+*If the order is a matter it is a Permutation.
-A formula for the number of possible combinations of R objects from a set of N objects is (n  r)=n!/r!(n-r)!, where n!=1*2*3*...*n& r<=n.
+*A combination is denoted by <math>^nC_r</math> or <math>\binom{n}{r}</math> or <math>C(n,r)</math>.
-This function will give the result is Error when
+*A formula for the number of possible combinations of <math>r</math> objects from a set of <math>n</math> objects is:
-. The N&R are non numeric
+ <math>\binom{n}{r}=\frac{n!}{r!(n-r)!}</math>
-. The N&R<0 or N<R
+where <math>n!=1*2*3*...*n </math> & <math>r \le n</math>.
-When we are giving the N&R values in decimals ,it will convert in to Integers.
+*This function will give Error Result when
+#The <math>n</math> & <math>r</math> are non numeric
+#The <math>n</math> & <math>r < 0 </math> or <math>n < r</math>
+*When we are giving the <math>n</math> & <math>r</math> 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 <math>r</math> is negative.
-*COMBIN(5.4,2)=10 is equivalent to COMBIN(5,2)
+==ZOS==
-*COMBIN(5,-2)=NAN, because R is negative.
+*The syntax is to calculate COMBIN in ZOS is <math>COMBIN(Number,NumberChosen)</math>
+**<math>Number</math> is the number of items.
+**<math>NumberChosen</math> 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.
+{{#ev:youtube|cQXPq6y8bOw|280|center|Combin}}
 ==Examples==
 {| id="TABLE3" class="SpreadSheet blue"
 |- class="even"
-| CHIDIST(x,df)
+| COMBIN(Number,NumberChosen)
-! x
+! Number
-! df
+! Numberchosen
 ! RESULT
 |-
 |- class="odd"
-|CHIDIST(18,2)
+|COMBIN(12,3)
-|18
+|12
-|2
+|3
-|0.0001234098
+|220
 |- class="even"
-|CHIDIST(15,1)
+|COMBIN(4,4)
-|15
+|4
+|4
 |1
-|0.0001075112
 |- class="odd"
-|CHIDIST(2,1)
+|COMBIN(4,0)
-|2
+|4
-|1
+|0
-|0.157299207050
-|- class="even"
-|CHIDIST(-2,1)
-|(-)2
 |1
-|error
-|- class="odd"
-|CHIDIST(2,-1)
-|2
-|(-)1
-|error
 |}
+ a=34!C!3
+COMBIN(PERMUT(34, 3n), 3) (For Big Integer) OR a=34n!P!3!C!3 = 7713313203904
+==Related Videos==
+{{#ev:youtube|Bzuj8ItKT5w|280|center|COMBIN}}
 ==See Also==
@@ Line 61: / Line 73: @@
 ==References==
-[http://en.wikipedia.org/wiki/Complex_number| Complex Numbers]
+[http://en.wikipedia.org/wiki/Combination  Combination]
+*[[Z_API_Functions | List of Main Z Functions]]
+*[[ Z3 |   Z3 home ]]

Difference between revisions of "Manuals/calci/COMBIN"

Latest revision as of 03:18, 24 February 2022

Contents

Description

ZOS

Examples

Related Videos

See Also

References

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