Difference between revisions of "Manuals/calci/COMBINATIONS"
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| − | + | <div style="font-size:30px">'''COMBINATIONS (Array,HowMany)'''</div><br/> | |
| + | *<math>Array </math> is the set of numbers. | ||
| + | *<math>HowMany</math> 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 <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. | ||
| + | *Also known as the binomial coefficient or choice number and read "n choose k" . | ||
| + | *<math>_nC_k =\binom{n}{k}= \frac{n!}{k!(n-k)!}</math>. | ||
| + | *Here COMBINATIONS shows the choices of the selected objects. | ||
| + | |||
| + | ==Examples== | ||
| + | 1.COMBINATIONS([3,8,12],2) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | |3|| 8 | ||
| + | |- | ||
| + | |3 || 12 | ||
| + | |- | ||
| + | |8 || 12 | ||
| + | |} | ||
| + | 2.COMBINATIONS([10,18,300,23,192],3) | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | |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== | ||
| + | |||
| + | {{#ev:youtube|v=iKy-d5_erhI|280|center|Combinations}} | ||
| + | |||
| + | ==See Also== | ||
| + | *[[Manuals/calci/BINOMIAL | BINOMIAL]] | ||
| + | *[[Manuals/calci/BINOMIALCOEFFICIENT | BINOMIALCOEFFICIENT ]] | ||
| + | |||
| + | ==References== | ||
| + | [http://mathworld.wolfram.com/Combination.html Combinations] | ||
| + | |||
| + | |||
| + | |||
| + | |||
| + | *[[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.
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.
,
is the described number of choice.
.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
See Also
References