# Order of Permutations (1 2 3 4 5 6 7): Explained

• math8
In summary, the conversation is discussing the correct notation for a permutation and its order. The confusion arises because the given example is not in cycle notation, but rather the argument and value of a single permutation. The correct notation should be (137)(265)(4) and the order of the permutation is 3. The conversation concludes that the given answer is correct and fits with the given notation.
math8
I am sure this is very simple but I m kind of confused here.

What is this product equal to and what's the order of the permutation?

(1 2 3 4 5 6 7) (3 6 7 4 2 5 1)

I thought it was (3 7 5 2 6 1 4) but I am reading somewhere that it should be (137)(265)(4) and hence has order 3.

Why is this "(3 7 5 2 6 1 4)" not correct? I mean I thought I had to start with the last cycle and do 3-->6, in the first cycle, 6-->7
and then 7-->4, in the first cycle, 4-->5,...

So I would get something like (3 7 5 ...

I am very confused here, help

That isn't cycle notation. Are you sure they didn't write this on two rows, like
(1 2 3 4 5 6 7)
(3 6 7 4 2 5 1)
The first row is just the argument of the permutation and the second row is it's value.
I.e. 1->3 2->6 3->7 4->4 5->2 6->5 7->1

Last edited:
Oh I see, so if it was a product of cycles, my answer would have been correct and the order of the product would be 7. But in this case, we just have the argument of a permutation and its value. So the question here is not to find the order of the product of two cycles but rather the order of the single permutation (given the argument and the value).
Is that correct?

math8 said:
Oh I see, so if it was a product of cycles, my answer would have been correct and the order of the product would be 7. But in this case, we just have the argument of a permutation and its value. So the question here is not to find the order of the product of two cycles but rather the order of the single permutation (given the argument and the value).
Is that correct?

It looks like that to me. It seems to fit with the given answer.

thanks.

## What is the order of permutations?

The order of permutations refers to the number of different ways a set of objects can be arranged. In this case, the set is (1 2 3 4 5 6 7) and the order is 7!, which is equal to 5040.

## How do you calculate the order of permutations?

The order of permutations can be calculated by taking the factorial of the number of objects in the set. In this case, 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040.

## What is the difference between permutations and combinations?

Permutations and combinations both involve selecting and arranging objects, but the main difference is that permutations take into account the order of the objects, while combinations do not. In other words, permutations are for ordered sets, while combinations are for unordered sets.

## What is the significance of the order of permutations?

The order of permutations is important in various fields such as mathematics, computer science, and statistics. It is used to calculate the number of possible outcomes in a given scenario, and is also used in probability calculations and in determining the complexity of algorithms.

## How can the order of permutations be represented?

The order of permutations can be represented in various ways, including using factorial notation (n!), exponential notation (n^n), and using a multiplication symbol between numbers (n x n-1 x n-2 ... x 2 x 1). In this case, the order of permutations (1 2 3 4 5 6 7) can be represented as 7!.

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