Permutation Help! [closed]

-3

$begingroup$

How many possible ways to organize a set of natural numbers 1,2,3 ..., 2n so that each even number is in sequence in the even place

combinatorics permutations

share|cite|improve this question

asked Jan 23 at 10:27

Viliam GlézlViliam Glézl

31

$endgroup$

closed as off-topic by José Carlos Santos, drhab, N. F. Taussig, Namaste, mrtaurho Jan 23 at 11:54

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – José Carlos Santos, drhab, N. F. Taussig, Namaste, mrtaurho

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You can first populate the even numbers. So that's the same as asking, "in how many ways can you order the even numbers between 1 and $2n$". And after that you can consider the odd numbers (put them to their places).
  $endgroup$
  – Matti P.
  Jan 23 at 10:31
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to Math.SE. Take a look at How to ask a good question at Math.SE. To avoid downvotes and closing you should add your own efforts to the question, and tell us where you got stuck.
  $endgroup$
  – drhab
  Jan 23 at 10:48
  

  
  
  
  

add a comment | 

-3

$begingroup$

How many possible ways to organize a set of natural numbers 1,2,3 ..., 2n so that each even number is in sequence in the even place

combinatorics permutations

share|cite|improve this question

asked Jan 23 at 10:27

Viliam GlézlViliam Glézl

31

$endgroup$

closed as off-topic by José Carlos Santos, drhab, N. F. Taussig, Namaste, mrtaurho Jan 23 at 11:54

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – José Carlos Santos, drhab, N. F. Taussig, Namaste, mrtaurho

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You can first populate the even numbers. So that's the same as asking, "in how many ways can you order the even numbers between 1 and $2n$". And after that you can consider the odd numbers (put them to their places).
  $endgroup$
  – Matti P.
  Jan 23 at 10:31
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to Math.SE. Take a look at How to ask a good question at Math.SE. To avoid downvotes and closing you should add your own efforts to the question, and tell us where you got stuck.
  $endgroup$
  – drhab
  Jan 23 at 10:48
  

  
  
  
  

add a comment | 

-3

-3

-3

$begingroup$

How many possible ways to organize a set of natural numbers 1,2,3 ..., 2n so that each even number is in sequence in the even place

combinatorics permutations

share|cite|improve this question

asked Jan 23 at 10:27

Viliam GlézlViliam Glézl

31

$endgroup$

How many possible ways to organize a set of natural numbers 1,2,3 ..., 2n so that each even number is in sequence in the even place

combinatorics permutations

combinatorics permutations

share|cite|improve this question

asked Jan 23 at 10:27

Viliam GlézlViliam Glézl

31

share|cite|improve this question

asked Jan 23 at 10:27

Viliam GlézlViliam Glézl

31

share|cite|improve this question

share|cite|improve this question

asked Jan 23 at 10:27

Viliam GlézlViliam Glézl

31

asked Jan 23 at 10:27

Viliam GlézlViliam Glézl

31

asked Jan 23 at 10:27

Viliam GlézlViliam Glézl

31

31

closed as off-topic by José Carlos Santos, drhab, N. F. Taussig, Namaste, mrtaurho Jan 23 at 11:54

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – José Carlos Santos, drhab, N. F. Taussig, Namaste, mrtaurho

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by José Carlos Santos, drhab, N. F. Taussig, Namaste, mrtaurho Jan 23 at 11:54

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – José Carlos Santos, drhab, N. F. Taussig, Namaste, mrtaurho

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You can first populate the even numbers. So that's the same as asking, "in how many ways can you order the even numbers between 1 and $2n$". And after that you can consider the odd numbers (put them to their places).
  $endgroup$
  – Matti P.
  Jan 23 at 10:31
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to Math.SE. Take a look at How to ask a good question at Math.SE. To avoid downvotes and closing you should add your own efforts to the question, and tell us where you got stuck.
  $endgroup$
  – drhab
  Jan 23 at 10:48
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You can first populate the even numbers. So that's the same as asking, "in how many ways can you order the even numbers between 1 and $2n$". And after that you can consider the odd numbers (put them to their places).
  $endgroup$
  – Matti P.
  Jan 23 at 10:31
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to Math.SE. Take a look at How to ask a good question at Math.SE. To avoid downvotes and closing you should add your own efforts to the question, and tell us where you got stuck.
  $endgroup$
  – drhab
  Jan 23 at 10:48
  

  
  
  
  

$begingroup$
You can first populate the even numbers. So that's the same as asking, "in how many ways can you order the even numbers between 1 and $2n$". And after that you can consider the odd numbers (put them to their places).
$endgroup$
– Matti P.
Jan 23 at 10:31

$begingroup$
You can first populate the even numbers. So that's the same as asking, "in how many ways can you order the even numbers between 1 and $2n$". And after that you can consider the odd numbers (put them to their places).
$endgroup$
– Matti P.
Jan 23 at 10:31

$begingroup$
Welcome to Math.SE. Take a look at How to ask a good question at Math.SE. To avoid downvotes and closing you should add your own efforts to the question, and tell us where you got stuck.
$endgroup$
– drhab
Jan 23 at 10:48

$begingroup$
Welcome to Math.SE. Take a look at How to ask a good question at Math.SE. To avoid downvotes and closing you should add your own efforts to the question, and tell us where you got stuck.
$endgroup$
– drhab
Jan 23 at 10:48

add a comment | 

2 Answers
2

active

oldest

votes

0

$begingroup$

since there are 2n numbers so there are n even numbers and n odd numbers

So all the n even numbers can be arranged at even places in n! ways and the odd numbers in n! ways at odd places

So the possible ways to arrange them is ( n! x n! ) ways.

share|cite|improve this answer

answered Jan 23 at 10:33

cognitivecognitive

264

$endgroup$

add a comment | 

0

$begingroup$

If all the even numbers are put on the even places, only the odd places are left for the odd numbers. Then the set of possibilities is the cartesian product of the sequences of the even numbers and that of the odd numbers treated separately. Thus:

n!n!

share|cite|improve this answer

answered Jan 23 at 10:31

ternaryternary

61

$endgroup$

add a comment | 

2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

0

$begingroup$

since there are 2n numbers so there are n even numbers and n odd numbers

So all the n even numbers can be arranged at even places in n! ways and the odd numbers in n! ways at odd places

So the possible ways to arrange them is ( n! x n! ) ways.

share|cite|improve this answer

answered Jan 23 at 10:33

cognitivecognitive

264

$endgroup$

add a comment | 

0

$begingroup$

since there are 2n numbers so there are n even numbers and n odd numbers

So all the n even numbers can be arranged at even places in n! ways and the odd numbers in n! ways at odd places

So the possible ways to arrange them is ( n! x n! ) ways.

share|cite|improve this answer

answered Jan 23 at 10:33

cognitivecognitive

264

$endgroup$

add a comment | 

0

0

0

$begingroup$

since there are 2n numbers so there are n even numbers and n odd numbers

So all the n even numbers can be arranged at even places in n! ways and the odd numbers in n! ways at odd places

So the possible ways to arrange them is ( n! x n! ) ways.

share|cite|improve this answer

answered Jan 23 at 10:33

cognitivecognitive

264

$endgroup$

since there are 2n numbers so there are n even numbers and n odd numbers

So all the n even numbers can be arranged at even places in n! ways and the odd numbers in n! ways at odd places

So the possible ways to arrange them is ( n! x n! ) ways.

share|cite|improve this answer

answered Jan 23 at 10:33

cognitivecognitive

264

share|cite|improve this answer

share|cite|improve this answer

answered Jan 23 at 10:33

cognitivecognitive

264

answered Jan 23 at 10:33

cognitivecognitive

264

answered Jan 23 at 10:33

cognitivecognitive

264

264

add a comment | 

add a comment | 

0

$begingroup$

If all the even numbers are put on the even places, only the odd places are left for the odd numbers. Then the set of possibilities is the cartesian product of the sequences of the even numbers and that of the odd numbers treated separately. Thus:

n!n!

share|cite|improve this answer

answered Jan 23 at 10:31

ternaryternary

61

$endgroup$

add a comment | 

0

$begingroup$

If all the even numbers are put on the even places, only the odd places are left for the odd numbers. Then the set of possibilities is the cartesian product of the sequences of the even numbers and that of the odd numbers treated separately. Thus:

n!n!

share|cite|improve this answer

answered Jan 23 at 10:31

ternaryternary

61

$endgroup$

add a comment | 

0

0

0

$begingroup$

If all the even numbers are put on the even places, only the odd places are left for the odd numbers. Then the set of possibilities is the cartesian product of the sequences of the even numbers and that of the odd numbers treated separately. Thus:

n!n!

share|cite|improve this answer

answered Jan 23 at 10:31

ternaryternary

61

$endgroup$

If all the even numbers are put on the even places, only the odd places are left for the odd numbers. Then the set of possibilities is the cartesian product of the sequences of the even numbers and that of the odd numbers treated separately. Thus:

n!n!

share|cite|improve this answer

answered Jan 23 at 10:31

ternaryternary

61

share|cite|improve this answer

share|cite|improve this answer

answered Jan 23 at 10:31

ternaryternary

61

answered Jan 23 at 10:31

ternaryternary

61

answered Jan 23 at 10:31

ternaryternary

61

61

add a comment | 

add a comment | 

This page is only for reference, If you need detailed information, please check here