Finding number of way to combine words with at least $1$ vowel












0












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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







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    0












    $begingroup$



    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







    share|cite|improve this question











    $endgroup$















      0












      0








      0





      $begingroup$



      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







      share|cite|improve this question











      $endgroup$





      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






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Jan 18 at 17:15









      N. F. Taussig

      44.5k103357




      44.5k103357










      asked Jan 18 at 16:24









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      36117






















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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 $88434-7290=81144$






          share|cite|improve this 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 $88434-7290=81144$






            share|cite|improve this answer











            $endgroup$


















              1












              $begingroup$

              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 $88434-7290=81144$






              share|cite|improve this answer











              $endgroup$
















                1












                1








                1





                $begingroup$

                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 $88434-7290=81144$






                share|cite|improve this answer











                $endgroup$



                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 $88434-7290=81144$







                share|cite|improve this answer














                share|cite|improve this answer



                share|cite|improve this answer








                edited Jan 18 at 17:22

























                answered Jan 18 at 16:38









                user289143user289143

                1,002313




                1,002313






























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