Dtjytyk

Applicability of Single Responsibility Principle

Roman Numeral Treatment of Suspensions

How does Loki do this?

Large drywall patch supports

System.debug(JSON.Serialize(o)) Not longer shows full string

Is this apparent Class Action settlement a spam message?

How does the UK government determine the size of a mandate?

Short story about space worker geeks who zone out by 'listening' to radiation from stars

Why does indent disappear in lists?

Can the discrete variable be a negative number?

How does it work when somebody invests in my business?

Is there a korbon needed for conversion?

Pole-zeros of a real-valued causal FIR system

How can I kill an app using Terminal?

Is expanding the research of a group into machine learning as a PhD student risky?

Opposite of a diet

How to safely derail a train during transit?

How long to clear the 'suck zone' of a turbofan after start is initiated?

How easy is it to start Magic from scratch?

How do I extract a value from a time formatted value in excel?

Do sorcerers' Subtle Spells require a skill check to be unseen?

A Rare Riley Riddle

Anatomically Correct Strange Women In Ponds Distributing Swords

Unreliable Magic - Is it worth it?

How many ways can $1$s and $2$s be arranged in a row such that there have always been more ones than twos. [closed]

How many sequences of lenght 2n, made of n “+1”s and n “-1”s and such that every partial summation of the first k terms is nonnegative, are there?In how many ways can an animal trainer arrange 5 lions and 4 tigers in a row so that no two lions are together?The number of ways to draw boundaries of constituencies, subject to constraintsn 1's and n 2'sHow many different ways can the numbers 1-9 be arranged in a 3x9 grid?How many ways can the integers 1,2,3,4,5,6 be arranged so that the 2 is adjacent to either 1 or 3?In how many ways can the letters in WONDERING be arranged with exactly two consecutive vowelsArrangement in a row (2 numbers)How many ways can four planes be arranged in space?In how many ways can n red balls and n blue balls be arranged such that number of red balls from left side is >= number of blue balls?In how many ways can $n$ dogs and $k$ cats be arranged in a row so that no two cats are adjacent?

2

0

$begingroup$

Find the number of ways in which $n$ ones and $n$ twos can be arranged in a row, such that up to any point in the row, the number of ones is more than or equal to the number of twos that have occurred so far.

---

Here's what i tried.

Let me arrange $n$ ones vertically in a column and $n$ ones horizontally in a row.

But this didn't get me anywhere.

Please help me.

combinatorics

share|cite|improve this question

edited Mar 15 at 15:53

user334732

4,32211240

asked Mar 6 at 8:05

jackyjacky

1,336816

$endgroup$

closed as off-topic by Eevee Trainer, Saad, Thomas Shelby, José Carlos Santos, mrtaurho Mar 16 at 20:55

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." – Saad, Thomas Shelby, mrtaurho

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

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Your question is not clear due to grammar problems, and the symbols $1',2'$ being confused with $1,2$. Try to correct them or use a diagram. If it is "applicable to a large audience", make sure that a large audience understands it in the first go.
  $endgroup$
  – астон вілла олоф мэллбэрг
  Mar 8 at 12:22
  
  
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  you seem to want to Catalan numbers: en.wikipedia.org/wiki/…
  $endgroup$
  – antkam
  Mar 8 at 14:26
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  See math.stackexchange.com/questions/1339700/…
  $endgroup$
  – Arnaud D.
  Mar 15 at 8:52
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I have tried to rewrite this to mean what I think you mean. I agree this asks for Catalan numbers but you want the $n-1$th Catalan number. Catalan numbers count the number of noncrossing partitions.
  $endgroup$
  – user334732
  Mar 15 at 15:59
  
  
  

  
  
  
  

add a comment | 

2

0

$begingroup$

Find the number of ways in which $n$ ones and $n$ twos can be arranged in a row, such that up to any point in the row, the number of ones is more than or equal to the number of twos that have occurred so far.

---

Here's what i tried.

Let me arrange $n$ ones vertically in a column and $n$ ones horizontally in a row.

But this didn't get me anywhere.

Please help me.

combinatorics

share|cite|improve this question

edited Mar 15 at 15:53

user334732

4,32211240

asked Mar 6 at 8:05

jackyjacky

1,336816

$endgroup$

closed as off-topic by Eevee Trainer, Saad, Thomas Shelby, José Carlos Santos, mrtaurho Mar 16 at 20:55

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." – Saad, Thomas Shelby, mrtaurho

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

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Your question is not clear due to grammar problems, and the symbols $1',2'$ being confused with $1,2$. Try to correct them or use a diagram. If it is "applicable to a large audience", make sure that a large audience understands it in the first go.
  $endgroup$
  – астон вілла олоф мэллбэрг
  Mar 8 at 12:22
  
  
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  you seem to want to Catalan numbers: en.wikipedia.org/wiki/…
  $endgroup$
  – antkam
  Mar 8 at 14:26
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  See math.stackexchange.com/questions/1339700/…
  $endgroup$
  – Arnaud D.
  Mar 15 at 8:52
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I have tried to rewrite this to mean what I think you mean. I agree this asks for Catalan numbers but you want the $n-1$th Catalan number. Catalan numbers count the number of noncrossing partitions.
  $endgroup$
  – user334732
  Mar 15 at 15:59
  
  
  

  
  
  
  

add a comment | 

$begingroup$

Find the number of ways in which $n$ ones and $n$ twos can be arranged in a row, such that up to any point in the row, the number of ones is more than or equal to the number of twos that have occurred so far.

---

Here's what i tried.

Let me arrange $n$ ones vertically in a column and $n$ ones horizontally in a row.

But this didn't get me anywhere.

Please help me.

combinatorics

share|cite|improve this question

edited Mar 15 at 15:53

user334732

4,32211240

asked Mar 6 at 8:05

jackyjacky

1,336816

$endgroup$

share|cite|improve this question

edited Mar 15 at 15:53

user334732

4,32211240

asked Mar 6 at 8:05

jackyjacky

1,336816

share|cite|improve this question

edited Mar 15 at 15:53

user334732

4,32211240

asked Mar 6 at 8:05

jackyjacky

1,336816

edited Mar 15 at 15:53

user334732

4,32211240

edited Mar 15 at 15:53

user334732

4,32211240

asked Mar 6 at 8:05

jackyjacky

1,336816

asked Mar 6 at 8:05

jackyjacky

1,336816

1 Answer
1

active

oldest

votes

1

$begingroup$

The answer is given by the Catalan number for n. It can be easily calculated from the formula (2n)!/((n+1)×n!×n!). For proof you can refer to various sources available on the internet.See https://en.m.wikipedia.org/wiki/Catalan_number#Proof_of_the_formula for proof

share|cite|improve this answer

answered Mar 12 at 8:32

User2003User2003

111

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Are you sure it's not the Catalan number for $n-1$?
  $endgroup$
  – user334732
  Mar 15 at 16:00
  

  
  
  
  

add a comment | 

1

$begingroup$

The answer is given by the Catalan number for n. It can be easily calculated from the formula (2n)!/((n+1)×n!×n!). For proof you can refer to various sources available on the internet.See https://en.m.wikipedia.org/wiki/Catalan_number#Proof_of_the_formula for proof

share|cite|improve this answer

answered Mar 12 at 8:32

User2003User2003

111

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Are you sure it's not the Catalan number for $n-1$?
  $endgroup$
  – user334732
  Mar 15 at 16:00
  

  
  
  
  

add a comment | 

1

$begingroup$

The answer is given by the Catalan number for n. It can be easily calculated from the formula (2n)!/((n+1)×n!×n!). For proof you can refer to various sources available on the internet.See https://en.m.wikipedia.org/wiki/Catalan_number#Proof_of_the_formula for proof

share|cite|improve this answer

answered Mar 12 at 8:32

User2003User2003

111

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Are you sure it's not the Catalan number for $n-1$?
  $endgroup$
  – user334732
  Mar 15 at 16:00
  

  
  
  
  

add a comment | 

$begingroup$

The answer is given by the Catalan number for n. It can be easily calculated from the formula (2n)!/((n+1)×n!×n!). For proof you can refer to various sources available on the internet.See https://en.m.wikipedia.org/wiki/Catalan_number#Proof_of_the_formula for proof

share|cite|improve this answer

answered Mar 12 at 8:32

User2003User2003

111

$endgroup$

share|cite|improve this answer

answered Mar 12 at 8:32

User2003User2003

111

answered Mar 12 at 8:32

User2003User2003

111

answered Mar 12 at 8:32

User2003User2003

111