Mixing
Finding number of way to combine words with at least $1$ vowel
$begingroup$
a) In an alphabet consisting of $18$ letters, how many "words" with word length $4$ is it possible to make when no consecutive letters can be equal?
I found this value to $88434$ (confirmed to be correct)
b) Assume the alphabet in a) consists of $10$ consonants and $8$ vowels. How many of the words from a) contain at least one vowel?
combinatorics
edited Jan 18 at 17:15
N. F. Taussig
44.5k103357
asked Jan 18 at 16:24
PamePame
36117
$endgroup$
add a comment |
$begingroup$
a) In an alphabet consisting of $18$ letters, how many "words" with word length $4$ is it possible to make when no consecutive letters can be equal?
I found this value to $88434$ (confirmed to be correct)
b) Assume the alphabet in a) consists of $10$ consonants and $8$ vowels. How many of the words from a) contain at least one vowel?
combinatorics
edited Jan 18 at 17:15
N. F. Taussig
44.5k103357
asked Jan 18 at 16:24
PamePame
36117
$endgroup$
add a comment |
$begingroup$
a) In an alphabet consisting of $18$ letters, how many "words" with word length $4$ is it possible to make when no consecutive letters can be equal?
I found this value to $88434$ (confirmed to be correct)
b) Assume the alphabet in a) consists of $10$ consonants and $8$ vowels. How many of the words from a) contain at least one vowel?
combinatorics
edited Jan 18 at 17:15
N. F. Taussig
44.5k103357
asked Jan 18 at 16:24
PamePame
36117
$endgroup$
a) In an alphabet consisting of $18$ letters, how many "words" with word length $4$ is it possible to make when no consecutive letters can be equal?
I found this value to $88434$ (confirmed to be correct)
b) Assume the alphabet in a) consists of $10$ consonants and $8$ vowels. How many of the words from a) contain at least one vowel?
combinatorics
combinatorics
edited Jan 18 at 17:15
N. F. Taussig
44.5k103357
asked Jan 18 at 16:24
PamePame
36117
edited Jan 18 at 17:15
N. F. Taussig
44.5k103357
asked Jan 18 at 16:24
PamePame
36117
edited Jan 18 at 17:15
N. F. Taussig
44.5k103357
edited Jan 18 at 17:15
N. F. Taussig
44.5k103357
edited Jan 18 at 17:15
N. F. Taussig
44.5k103357
44.5k103357
asked Jan 18 at 16:24
PamePame
36117
asked Jan 18 at 16:24
PamePame
36117
asked Jan 18 at 16:24
PamePame
36117
36117
add a comment |
add a comment |
1 Answer
1
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$begingroup$
You can count how many words has all consonants and subtract it from the whole possible words in a).
Thus we have $10 cdot 9 cdot 9 cdot 9=7290$ words with all consonants.
Now the number of words with a least one vowel are $88434-7290=81144$
answered Jan 18 at 16:38
user289143user289143
1,002313
$endgroup$
add a comment |
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1 Answer
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1 Answer
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$begingroup$
You can count how many words has all consonants and subtract it from the whole possible words in a).
Thus we have $10 cdot 9 cdot 9 cdot 9=7290$ words with all consonants.
Now the number of words with a least one vowel are $88434-7290=81144$
answered Jan 18 at 16:38
user289143user289143
1,002313
$endgroup$
add a comment |
$begingroup$
You can count how many words has all consonants and subtract it from the whole possible words in a).
Thus we have $10 cdot 9 cdot 9 cdot 9=7290$ words with all consonants.
Now the number of words with a least one vowel are $88434-7290=81144$
answered Jan 18 at 16:38
user289143user289143
1,002313
$endgroup$
add a comment |
$begingroup$
You can count how many words has all consonants and subtract it from the whole possible words in a).
Thus we have $10 cdot 9 cdot 9 cdot 9=7290$ words with all consonants.
Now the number of words with a least one vowel are $88434-7290=81144$
answered Jan 18 at 16:38
user289143user289143
1,002313
$endgroup$
You can count how many words has all consonants and subtract it from the whole possible words in a).
Thus we have $10 cdot 9 cdot 9 cdot 9=7290$ words with all consonants.
Now the number of words with a least one vowel are $88434-7290=81144$
answered Jan 18 at 16:38
user289143user289143
1,002313
edited Jan 18 at 17:22
answered Jan 18 at 16:38
user289143user289143
1,002313
answered Jan 18 at 16:38
user289143user289143
1,002313
answered Jan 18 at 16:38
user289143user289143
1,002313
1,002313
add a comment |
add a comment |
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