Combinations / Sets of objects

In summary, combinations are a selection of objects where the order does not matter, while permutations are a selection of objects where the order does matter. The number of combinations can be calculated using the formula nCr = n! / (r! * (n-r)!), and the number of permutations can be calculated using the formula nPr = n! / (n-r)!. Combinations and permutations can also be repeated, with different formulas to use depending on whether repetition is allowed or not. They are used in various fields such as mathematics, computer science, and statistics to solve problems involving selecting and arranging objects, as well as in probability and statistics. Examples of combinations include choosing a group of students for a project, selecting toppings for a pizza
  • #1
arno100
1
0
Hi,

I am looking for a solution that generates combinations of objects from a series of objects in a set. For example, {Apple, Pear, Orange} should bring back
Apple
Pear
Orange
Apple, Pear
Apple, Pear, Orange,
Apple, Orange
...

Items in the series should not repeat (i.e. Apple, Orange / Orange, Apple should only appear once). Any online generators anybody can suggest? Or, material I can use to figure this out?

Many thanks
 
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  • #2
You forgot "Pear, Orange", the formula is 2^n with n is the number of elements in the set. Beware that 2^n also includes an empty set.
 

FAQ: Combinations / Sets of objects

What are combinations?

Combinations refer to the different ways in which a set of objects can be arranged or selected without any regard to the order in which they are chosen.

How do you calculate the number of combinations?

The number of combinations can be calculated using the formula nCr = n! / (r! * (n-r)!), where n represents the total number of objects and r represents the number of objects being selected.

What is the difference between combinations and permutations?

Combinations do not take into account the order in which objects are selected, while permutations do. This means that in combinations, ABC and CBA would be considered the same, but in permutations they would be different.

How can combinations be useful in real life?

Combinations can be useful in various fields such as statistics, probability, and genetics. They can be used to determine the likelihood of certain outcomes or to analyze data sets.

Can combinations be applied to non-numerical objects?

Yes, combinations can be applied to non-numerical objects as long as they can be counted and arranged in different ways. For example, combinations can be used to determine the number of different outfits that can be created from a set of clothing items.

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