Difference between revisions of "Manuals/calci/COMBINATIONS"

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*In <math>COMBINATIONS (Array,HowMany)</math>,<math>Array</math> is the set of numbers and <math>Howmany</math> is the described number of choice.
 
*In <math>COMBINATIONS (Array,HowMany)</math>,<math>Array</math> is the set of numbers and <math>Howmany</math> is the described number of choice.
 
*The number of ways of picking k unordered outcomes from n possibilities.  
 
*The number of ways of picking k unordered outcomes from n possibilities.  
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*Also known as the binomial coefficient or choice number and read "n choose k," <math>\binom{n}{k}= \binom{n-1}{k-1} +\binom{n-1}{k}</math> nck= Formula.
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*Also known as the binomial coefficient or choice number and read "n choose k" .
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*<math>_nC_k =\binom{n}{k}= \frac{n!}{k!(n-k)!}</math>.
 
*Here COMBINATIONS shows the choices of the selected objects.
 
*Here COMBINATIONS shows the choices of the selected objects.
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==Examples==
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1.COMBINATIONS([3,8,12],2)
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{| class="wikitable"
 +
|-
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|3|| 8
 +
|-
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|3 || 12
 +
|-
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|8 || 12
 +
|}
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2.COMBINATIONS([10,18,300,23,192],3)
 +
{| class="wikitable"
 +
|-
 +
|10||18||300
 +
|-
 +
|10 ||18||23
 +
|-
 +
|10||18||192
 +
|-
 +
|10||300||23
 +
|-
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|10 ||300||192
 +
|-
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|10 || 23||192
 +
|-
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|18||300||23
 +
|-
 +
|18 ||300||192
 +
|-
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|18||23||192
 +
|-
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|300||23||192
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|}
 +
 +
 +
==Related Videos==
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 +
{{#ev:youtube|v=iKy-d5_erhI|280|center|Combinations}}
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 +
==See Also==
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*[[Manuals/calci/BINOMIAL | BINOMIAL]]
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*[[Manuals/calci/BINOMIALCOEFFICIENT  | BINOMIALCOEFFICIENT ]]
 +
 +
==References==
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[http://mathworld.wolfram.com/Combination.html Combinations]
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 +
 +
 +
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*[[Z_API_Functions | List of Main Z Functions]]
 +
 +
*[[ Z3 |  Z3 home ]]

Latest revision as of 15:05, 10 December 2018

COMBINATIONS (Array,HowMany)


  • is the set of numbers.
  • is the number of choices.

Description

  • This function shows the combination of the given numbers.
  • A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected.
  • In , is the set of numbers and is the described number of choice.
  • The number of ways of picking k unordered outcomes from n possibilities.
  • Also known as the binomial coefficient or choice number and read "n choose k" .
  • .
  • Here COMBINATIONS shows the choices of the selected objects.

Examples

1.COMBINATIONS([3,8,12],2)

3 8
3 12
8 12

2.COMBINATIONS([10,18,300,23,192],3)

10 18 300
10 18 23
10 18 192
10 300 23
10 300 192
10 23 192
18 300 23
18 300 192
18 23 192
300 23 192


Related Videos

Combinations

See Also

References

Combinations



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