Say I have 5 computers. How many permutations are available?

  • Context: High School 
  • Thread starter Thread starter Poweranimals
  • Start date Start date
  • Tags Tags
    Computers Permutations
Click For Summary

Discussion Overview

The discussion revolves around the concept of permutations, specifically in the context of arranging computers in a linear network and later extending to the arrangement of programs. Participants explore the mathematical principles behind permutations and combinations, raising questions about the implications of the term "linear" and how it relates to different types of arrangements.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant asks about the number of permutations available for five computers, prompting a need for clarification on what is being permuted.
  • Another participant states that the permutations of five computers can be calculated as 120, referencing the basic principle of permutations.
  • A participant expresses confusion about the relevance of the term "linear" in the context of the arrangement of computers.
  • Some participants discuss the implications of a linear arrangement versus other types of arrangements, such as tree or circular networks, suggesting that the linear aspect may influence the number of arrangements.
  • There is a proposal regarding the arrangement of programs, where one participant suggests a multiplication approach to find the number of ways to arrange four out of twenty programs.
  • Another participant corrects this approach, stating that combinations should be used instead of permutations for the programs question, providing the formula for combinations.
  • Some participants argue about the distinction between permutations and combinations, with one asserting that the original question specifically asked for permutations.
  • There is a recognition that the two questions (computers and programs) are different in nature, with agreement that the correct approach varies based on the context.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of the term "linear" and its mathematical implications. There is no consensus on the best approach to the programs question, with some advocating for permutations and others for combinations. The discussion remains unresolved regarding the implications of the linear arrangement on the number of permutations.

Contextual Notes

Some participants note that the term "linear" may not have a clear mathematical definition in this context, leading to confusion. The discussion also highlights the difference between permutations and combinations, with unresolved mathematical steps in the transition from one question to the other.

Poweranimals
Messages
68
Reaction score
0
Say I have 5 computers. How many permutations are available?
 
Physics news on Phys.org
Erm. that needs more information. permutations of what?
 
Five computers are to be wired in a linear network.
 
And? That doesn't answer the question.
 
permutations of the five computers
 
So you want to know how many ways there are to order five objects ? Well, that is very elementary, and it is 120, If you want to know more try reading about permutations and such and factorials.
 
Thanks. I guess the "linear" thing threw me off.

So would I be correct in assuming, that if I had twenty different programs, and could only access four of them at a time, that I would multiply 20 X 19 X 18 X 17; which equals 16,279,200 to find out many different ways I could arrange them?

If so, I think I got the hang of it.
 
half if not all of the point of my reply was that in saying you have a linear network does not mean the slightest thing to me mathematically. My answer has no bearing on whether or not they are linear or arranged in the shape of a quincunx.
 
I believe the linear part is probably useful to distinguish the arrangement from say, a 'tree network', where you may have to designate masters and slaves; or a circular network, where you would have only 24 arrangements. I'm sure 'linear' was meant in a homotopic sense.
 
  • #10
as a tree and a straight line are homotopic, to a point, I don't think so.
 
  • #11
Yeah, that's right. Okay, so that's not what I meant, but you get the idea. 'Linear' is like n-pentane, and 2,2 -dimethylpropane is a 'tree', while cyclopentane is a 'circle'.
 
  • #12
About the programs question (it may be alittle late now sorry) but you have to use a equation for combination. the equation is C(n,r)=n!/(n-r)!r!. If you not familiar with this the ! mean factorials. N represents total number of thing and in this case it would be 20 and r represents the restriction which would be 4.

You new equation will be C(20,4)=20!/(20-4)!4!

Go from there and if you need any help email me
 
  • #13
No, the OP specifically asked about permutations. He was correct that he needed to use 20!/(20-4)!= 20!/16!= 20(19)(18)(17). Dividing by 4! would count number of different ways without including permutations of the same 4 programs.
 
  • #14
It asked for Per. on the first Question but on the program Q. it wouldn't matter which program started with which one. It would just want tto find out how many different 4 combination could be used in the the process.
 
  • #15
Well, that makes no sense, but since this is a THREE year old post I don't suppose it matters.
 
  • #16
Ya it doesn't matter but i had the Question on my test the other day and got it right so i thought i would share it. Its kinda hard to explain on the thread.
 
  • #17
ProfessorMan said:
It asked for Per. on the first Question but on the program Q. it wouldn't matter which program started with which one. It would just want tto find out how many different 4 combination could be used in the the process.

You are quite correct. The two questions were different.

And giving the correct answer to a problem, however old it may be, is always good.
 

Similar threads

Undergrad About permutation acting on the Identity matrix
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Permutations written as product of 2-cycles
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Subgroup axioms for a symmetric group
  • · Replies 1 ·
Replies
1
Views
1K
High School Determinant of a transposed matrix
  • · Replies 3 ·
Replies
3
Views
3K
MHB LR decomposition with column pivoting
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Basic Question: Order of permutations in Sn
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Differences between left vs right actions in some group theory questions
  • · Replies 1 ·
Replies
1
Views
2K
High School Is it invalid to redefine the sgn function in this way in a proof?
  • · Replies 15 ·
Replies
15
Views
5K
Graduate How Can You Find the Number of Conjugation Permutations in a Group?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad How Do You Calculate the Square of a Permutation Matrix?
  • · Replies 6 ·
Replies
6
Views
8K