Number of ways a sequence can be arranged to meet the required condition [closed]

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I toss a coin 15 times and I obtain a strings of Heads(represented by H) and Tails(represented by T). I want to find the number of sequences which can be found such that there are 2 HH, 3 HT , 4 TH and 4 TT subsequences. How do I proceed?



One example of such a sequence can be TTTHHTHTTTHHTTH




combinatorics permutations combinations




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closed as off-topic by Mostafa Ayaz, Jyrki Lahtonen, Shailesh, Cesareo, Parcly Taxel Jul 18 at 13:51


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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Mostafa Ayaz, Jyrki Lahtonen, Shailesh, Cesareo, Parcly Taxel
If this question can be reworded to fit the rules in the help center, please edit the question.
















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    I toss a coin 15 times and I obtain a strings of Heads(represented by H) and Tails(represented by T). I want to find the number of sequences which can be found such that there are 2 HH, 3 HT , 4 TH and 4 TT subsequences. How do I proceed?



    One example of such a sequence can be TTTHHTHTTTHHTTH




    combinatorics permutations combinations




    share|cite|improve this question













    closed as off-topic by Mostafa Ayaz, Jyrki Lahtonen, Shailesh, Cesareo, Parcly Taxel Jul 18 at 13:51


    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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Mostafa Ayaz, Jyrki Lahtonen, Shailesh, Cesareo, Parcly Taxel
    If this question can be reworded to fit the rules in the help center, please edit the question.














      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      I toss a coin 15 times and I obtain a strings of Heads(represented by H) and Tails(represented by T). I want to find the number of sequences which can be found such that there are 2 HH, 3 HT , 4 TH and 4 TT subsequences. How do I proceed?



      One example of such a sequence can be TTTHHTHTTTHHTTH




      combinatorics permutations combinations




      share|cite|improve this question













      I toss a coin 15 times and I obtain a strings of Heads(represented by H) and Tails(represented by T). I want to find the number of sequences which can be found such that there are 2 HH, 3 HT , 4 TH and 4 TT subsequences. How do I proceed?



      One example of such a sequence can be TTTHHTHTTTHHTTH





      combinatorics permutations combinations





      share|cite|improve this question












      share|cite|improve this question




      share|cite|improve this question








      edited Jul 29 at 9:48
























      asked Jul 18 at 5:54









      saisanjeev

      379210




      379210




      closed as off-topic by Mostafa Ayaz, Jyrki Lahtonen, Shailesh, Cesareo, Parcly Taxel Jul 18 at 13:51


      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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Mostafa Ayaz, Jyrki Lahtonen, Shailesh, Cesareo, Parcly Taxel
      If this question can be reworded to fit the rules in the help center, please edit the question.




      closed as off-topic by Mostafa Ayaz, Jyrki Lahtonen, Shailesh, Cesareo, Parcly Taxel Jul 18 at 13:51


      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 improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Mostafa Ayaz, Jyrki Lahtonen, Shailesh, Cesareo, Parcly Taxel
      If this question can be reworded to fit the rules in the help center, please edit the question.




















          1 Answer
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          Any sequence with 3 $HT$s and 2 $TH$s must have the form
          $$H^aT^bH^cT^dH^e$$
          where $a,ldots,e$ are positive integers, and $H^a$ represents
          a sequence of $a$ consecutive heads etc. You need to find
          all possible triples $(a,c,e)$ yielding 5 $HH$s and
          all possible pairs $(b,d)$ yielding 4 $TT$s.






          share|cite|improve this answer





















          • The sequence I have mentioned in the question doesn't seem to follow the pattern you have mentioned...
            – saisanjeev
            Jul 23 at 10:55










          • Your sequence does not have $2$ $TH$s. @saisanjeev
            – Lord Shark the Unknown
            Jul 23 at 14:58











          • I am extremely sorry edited the question...
            – saisanjeev
            Jul 29 at 9:48

















          1 Answer
          1






          active

          oldest

          votes








          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes








          up vote
          2
          down vote













          Any sequence with 3 $HT$s and 2 $TH$s must have the form
          $$H^aT^bH^cT^dH^e$$
          where $a,ldots,e$ are positive integers, and $H^a$ represents
          a sequence of $a$ consecutive heads etc. You need to find
          all possible triples $(a,c,e)$ yielding 5 $HH$s and
          all possible pairs $(b,d)$ yielding 4 $TT$s.






          share|cite|improve this answer





















          • The sequence I have mentioned in the question doesn't seem to follow the pattern you have mentioned...
            – saisanjeev
            Jul 23 at 10:55










          • Your sequence does not have $2$ $TH$s. @saisanjeev
            – Lord Shark the Unknown
            Jul 23 at 14:58











          • I am extremely sorry edited the question...
            – saisanjeev
            Jul 29 at 9:48














          up vote
          2
          down vote













          Any sequence with 3 $HT$s and 2 $TH$s must have the form
          $$H^aT^bH^cT^dH^e$$
          where $a,ldots,e$ are positive integers, and $H^a$ represents
          a sequence of $a$ consecutive heads etc. You need to find
          all possible triples $(a,c,e)$ yielding 5 $HH$s and
          all possible pairs $(b,d)$ yielding 4 $TT$s.






          share|cite|improve this answer





















          • The sequence I have mentioned in the question doesn't seem to follow the pattern you have mentioned...
            – saisanjeev
            Jul 23 at 10:55










          • Your sequence does not have $2$ $TH$s. @saisanjeev
            – Lord Shark the Unknown
            Jul 23 at 14:58











          • I am extremely sorry edited the question...
            – saisanjeev
            Jul 29 at 9:48












          up vote
          2
          down vote










          up vote
          2
          down vote









          Any sequence with 3 $HT$s and 2 $TH$s must have the form
          $$H^aT^bH^cT^dH^e$$
          where $a,ldots,e$ are positive integers, and $H^a$ represents
          a sequence of $a$ consecutive heads etc. You need to find
          all possible triples $(a,c,e)$ yielding 5 $HH$s and
          all possible pairs $(b,d)$ yielding 4 $TT$s.






          share|cite|improve this answer













          Any sequence with 3 $HT$s and 2 $TH$s must have the form
          $$H^aT^bH^cT^dH^e$$
          where $a,ldots,e$ are positive integers, and $H^a$ represents
          a sequence of $a$ consecutive heads etc. You need to find
          all possible triples $(a,c,e)$ yielding 5 $HH$s and
          all possible pairs $(b,d)$ yielding 4 $TT$s.







          share|cite|improve this answer













          share|cite|improve this answer



          share|cite|improve this answer











          answered Jul 18 at 5:59









          Lord Shark the Unknown

          85.5k951112




          85.5k951112











          • The sequence I have mentioned in the question doesn't seem to follow the pattern you have mentioned...
            – saisanjeev
            Jul 23 at 10:55










          • Your sequence does not have $2$ $TH$s. @saisanjeev
            – Lord Shark the Unknown
            Jul 23 at 14:58











          • I am extremely sorry edited the question...
            – saisanjeev
            Jul 29 at 9:48
















          • The sequence I have mentioned in the question doesn't seem to follow the pattern you have mentioned...
            – saisanjeev
            Jul 23 at 10:55










          • Your sequence does not have $2$ $TH$s. @saisanjeev
            – Lord Shark the Unknown
            Jul 23 at 14:58











          • I am extremely sorry edited the question...
            – saisanjeev
            Jul 29 at 9:48















          The sequence I have mentioned in the question doesn't seem to follow the pattern you have mentioned...
          – saisanjeev
          Jul 23 at 10:55




          The sequence I have mentioned in the question doesn't seem to follow the pattern you have mentioned...
          – saisanjeev
          Jul 23 at 10:55












          Your sequence does not have $2$ $TH$s. @saisanjeev
          – Lord Shark the Unknown
          Jul 23 at 14:58





          Your sequence does not have $2$ $TH$s. @saisanjeev
          – Lord Shark the Unknown
          Jul 23 at 14:58













          I am extremely sorry edited the question...
          – saisanjeev
          Jul 29 at 9:48




          I am extremely sorry edited the question...
          – saisanjeev
          Jul 29 at 9:48


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