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The grouping of a subset of a set of items where the order does not matter is called a combination. One such example is the UK's National Lotto where 6 numbers have to be chosen from the 59 numbers 1-59).

If there are n different items and a subset of r of them are chosen where the order of choosing does not matter then the number of combinations is given by:

nCr = n!/((n-r)!r!)

where n! means "n factorial" - the product of all numbers 1 × 2 × ... × n; 0! is defined to be 1.

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Where the order of selection does matter, it is called a permutation. One such example would be the order of the first three runners in a race.

If there are n different items and a subset of r of them are chosen where the order of choosing does matter, then the number of permutations is given by:

nPr = n!/(n-r)!

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Q: What is a grouping of objects or events in which order does not matter?
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What is a grouping of objects where order does not matter?

They are sets of objects.


An arrangement of a set of items or events in which the order does not matter?

A combination. If the order does matter, the word is permutation.


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A permutation is an arrangement of objects in some specific order. Permutations are regarded as ordered elements. A selection in which order is not important is called a combination. Combinations are regarded as sets. For example, if there is a group of 3 different colored balls, then any group of 2 balls selected from it will be considered as a combination, whereas the different arrangements of every combination will be considered as a permutation.


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How many ways are there to pick n objects from n objects if order does matter?

There is a mathematical function called "factorial", and it is denoted by "!" (the exclamation mark). The factorial is when you multiply a number by every number before it, all the way down to 1. Eg: 5! = 5*4*3*2*1=120 So, when you choose n objects in random order, at first you have n choices. After that, you have n-1 choices left, and after that, then you have n-2 choices left, and so on. So the answer to the question "How many ways are there to pick n objects from n objects if order does not matter is: n! where n! = n*(n-1)*(n-2)*(n-3)*(n-4) . . . (3)*(2)*(1). * * * * * That is the number if the order DOES matter. If the order does NOT matter, as the question requires, the answer is 1.


What is an organism that groups between phylum and order?

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What is an avoider?

An avoider is a person who intentionally avoids things, or a vessel in which objects are carried away in order to avoid other objects.


If the phylum is broken down into classes what is the next grouping?

If the phylum is broken down into classes, the next grouping would be orders. After orders, the next grouping would be families, followed by genera (singular: genus), and finally species.


What is the importance of grouping plants?

So that plants can be so easy to be classified according to their order.


What is the next higher group to a family in the taxonomic hierarchial system for grouping organisms?

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What is a word for an orderly grouping that begins with the letter a?

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