How many n-letter words are there, such that number of letters “a” is even? [closed]
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How many n-letter words (made of letters from 25-letter english alphabet) are there, such that number of letters "a" is even? ("a" appears even number of times in a word).
I'm trying to create recursive formula, but with no success.
combinatorics recursion combinatorics-on-words
edited Dec 20 '18 at 15:34
Maria Mazur
50k1361125
asked Dec 20 '18 at 13:05
lellerleller
715
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closed as off-topic by Did, mrtaurho, Saad, user91500, Lord_Farin Dec 24 '18 at 9:07
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." – Did, mrtaurho, Saad, user91500, Lord_Farin
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
How many n-letter words (made of letters from 25-letter english alphabet) are there, such that number of letters "a" is even? ("a" appears even number of times in a word).
I'm trying to create recursive formula, but with no success.
combinatorics recursion combinatorics-on-words
edited Dec 20 '18 at 15:34
Maria Mazur
50k1361125
asked Dec 20 '18 at 13:05
lellerleller
715
$endgroup$
closed as off-topic by Did, mrtaurho, Saad, user91500, Lord_Farin Dec 24 '18 at 9:07
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." – Did, mrtaurho, Saad, user91500, Lord_Farin
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
If we have a "good" word of length $n-1$, how many letters can we append to make a good word of length $n$? Same question if we have a "bad" word of length $n-1$.
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– lulu
Dec 20 '18 at 13:08
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What happened to the missing letter?
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– paw88789
Dec 20 '18 at 15:56
$begingroup$
The same question, with two other letters instead of 24, is here
$endgroup$
– Ross Millikan
Dec 20 '18 at 16:06
$begingroup$
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.
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– Did
Dec 23 '18 at 21:34
add a comment |
$begingroup$
How many n-letter words (made of letters from 25-letter english alphabet) are there, such that number of letters "a" is even? ("a" appears even number of times in a word).
I'm trying to create recursive formula, but with no success.
combinatorics recursion combinatorics-on-words
edited Dec 20 '18 at 15:34
Maria Mazur
50k1361125
asked Dec 20 '18 at 13:05
lellerleller
715
$endgroup$
How many n-letter words (made of letters from 25-letter english alphabet) are there, such that number of letters "a" is even? ("a" appears even number of times in a word).
I'm trying to create recursive formula, but with no success.
combinatorics recursion combinatorics-on-words
combinatorics recursion combinatorics-on-words
edited Dec 20 '18 at 15:34
Maria Mazur
50k1361125
asked Dec 20 '18 at 13:05
lellerleller
715
edited Dec 20 '18 at 15:34
Maria Mazur
50k1361125
asked Dec 20 '18 at 13:05
lellerleller
715
edited Dec 20 '18 at 15:34
Maria Mazur
50k1361125
edited Dec 20 '18 at 15:34
Maria Mazur
50k1361125
edited Dec 20 '18 at 15:34
Maria Mazur
50k1361125
50k1361125
asked Dec 20 '18 at 13:05
lellerleller
715
asked Dec 20 '18 at 13:05
lellerleller
715
asked Dec 20 '18 at 13:05
lellerleller
715
715
closed as off-topic by Did, mrtaurho, Saad, user91500, Lord_Farin Dec 24 '18 at 9:07
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." – Did, mrtaurho, Saad, user91500, Lord_Farin
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Did, mrtaurho, Saad, user91500, Lord_Farin Dec 24 '18 at 9:07
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." – Did, mrtaurho, Saad, user91500, Lord_Farin
If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
If we have a "good" word of length $n-1$, how many letters can we append to make a good word of length $n$? Same question if we have a "bad" word of length $n-1$.
$endgroup$
– lulu
Dec 20 '18 at 13:08
$begingroup$
What happened to the missing letter?
$endgroup$
– paw88789
Dec 20 '18 at 15:56
$begingroup$
The same question, with two other letters instead of 24, is here
$endgroup$
– Ross Millikan
Dec 20 '18 at 16:06
$begingroup$
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.
$endgroup$
– Did
Dec 23 '18 at 21:34
add a comment |
$begingroup$
If we have a "good" word of length $n-1$, how many letters can we append to make a good word of length $n$? Same question if we have a "bad" word of length $n-1$.
$endgroup$
– lulu
Dec 20 '18 at 13:08
$begingroup$
What happened to the missing letter?
$endgroup$
– paw88789
Dec 20 '18 at 15:56
$begingroup$
The same question, with two other letters instead of 24, is here
$endgroup$
– Ross Millikan
Dec 20 '18 at 16:06
$begingroup$
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.
$endgroup$
– Did
Dec 23 '18 at 21:34
$begingroup$
If we have a "good" word of length $n-1$, how many letters can we append to make a good word of length $n$? Same question if we have a "bad" word of length $n-1$.
$endgroup$
– lulu
Dec 20 '18 at 13:08
$begingroup$
If we have a "good" word of length $n-1$, how many letters can we append to make a good word of length $n$? Same question if we have a "bad" word of length $n-1$.
$endgroup$
– lulu
Dec 20 '18 at 13:08
$begingroup$
What happened to the missing letter?
$endgroup$
– paw88789
Dec 20 '18 at 15:56
$begingroup$
What happened to the missing letter?
$endgroup$
– paw88789
Dec 20 '18 at 15:56
$begingroup$
The same question, with two other letters instead of 24, is here
$endgroup$
– Ross Millikan
Dec 20 '18 at 16:06
$begingroup$
The same question, with two other letters instead of 24, is here
$endgroup$
– Ross Millikan
Dec 20 '18 at 16:06
$begingroup$
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.
$endgroup$
– Did
Dec 23 '18 at 21:34
$begingroup$
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.
$endgroup$
– Did
Dec 23 '18 at 21:34
add a comment |
1 Answer
1
active
oldest
votes
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Let $o_n$ be a number of n-lenght words with odd number of $a$ and
let $e_n$ be a number of n-lenght words with even number of $a$.
Then $o_n+e_n = 25^n$ and $$ e_{n+1} = o_n+ 24e_n$$
that is if first letter is $a$ then in the rest of a word must be odd number of $a$ and if first letter is not $a$ then the number of even $a$ is the same as in a $n$-lenght word times 24 (since we have 24 choises for first number) .
answered Dec 20 '18 at 13:08
Maria MazurMaria Mazur
50k1361125
$endgroup$
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Let $o_n$ be a number of n-lenght words with odd number of $a$ and
let $e_n$ be a number of n-lenght words with even number of $a$.
Then $o_n+e_n = 25^n$ and $$ e_{n+1} = o_n+ 24e_n$$
that is if first letter is $a$ then in the rest of a word must be odd number of $a$ and if first letter is not $a$ then the number of even $a$ is the same as in a $n$-lenght word times 24 (since we have 24 choises for first number) .
answered Dec 20 '18 at 13:08
Maria MazurMaria Mazur
50k1361125
$endgroup$
add a comment |
$begingroup$
Let $o_n$ be a number of n-lenght words with odd number of $a$ and
let $e_n$ be a number of n-lenght words with even number of $a$.
Then $o_n+e_n = 25^n$ and $$ e_{n+1} = o_n+ 24e_n$$
that is if first letter is $a$ then in the rest of a word must be odd number of $a$ and if first letter is not $a$ then the number of even $a$ is the same as in a $n$-lenght word times 24 (since we have 24 choises for first number) .
answered Dec 20 '18 at 13:08
Maria MazurMaria Mazur
50k1361125
$endgroup$
add a comment |
$begingroup$
Let $o_n$ be a number of n-lenght words with odd number of $a$ and
let $e_n$ be a number of n-lenght words with even number of $a$.
Then $o_n+e_n = 25^n$ and $$ e_{n+1} = o_n+ 24e_n$$
that is if first letter is $a$ then in the rest of a word must be odd number of $a$ and if first letter is not $a$ then the number of even $a$ is the same as in a $n$-lenght word times 24 (since we have 24 choises for first number) .
answered Dec 20 '18 at 13:08
Maria MazurMaria Mazur
50k1361125
$endgroup$
Let $o_n$ be a number of n-lenght words with odd number of $a$ and
let $e_n$ be a number of n-lenght words with even number of $a$.
Then $o_n+e_n = 25^n$ and $$ e_{n+1} = o_n+ 24e_n$$
that is if first letter is $a$ then in the rest of a word must be odd number of $a$ and if first letter is not $a$ then the number of even $a$ is the same as in a $n$-lenght word times 24 (since we have 24 choises for first number) .
answered Dec 20 '18 at 13:08
Maria MazurMaria Mazur
50k1361125
edited Dec 20 '18 at 13:30
answered Dec 20 '18 at 13:08
Maria MazurMaria Mazur
50k1361125
answered Dec 20 '18 at 13:08
Maria MazurMaria Mazur
50k1361125
answered Dec 20 '18 at 13:08
Maria MazurMaria Mazur
50k1361125
50k1361125
add a comment |
add a comment |
$begingroup$
If we have a "good" word of length $n-1$, how many letters can we append to make a good word of length $n$? Same question if we have a "bad" word of length $n-1$.
$endgroup$
– lulu
Dec 20 '18 at 13:08
$begingroup$
What happened to the missing letter?
$endgroup$
– paw88789
Dec 20 '18 at 15:56
$begingroup$
The same question, with two other letters instead of 24, is here
$endgroup$
– Ross Millikan
Dec 20 '18 at 16:06
$begingroup$
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.
$endgroup$
– Did
Dec 23 '18 at 21:34