Given TECHNOLOGY , find number of distinguishable ways the letters can be arranged in which letters T,E and N...











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Given TECHNOLOGY , find number of distinguishable ways the letters can be arranged in which letters T,E and N are together



This is my working-



$3! cdot frac{7!}{2!} $



is this correct ?










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put on hold as off-topic by Rushabh Mehta, MisterRiemann, NCh, Shailesh, John B Dec 1 at 0:45


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." – Rushabh Mehta, MisterRiemann, NCh, Shailesh

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









  • 5




    Solutions to such exercises should usually be presented in such a way that one can understand how you reached the answer, i.e. you should explain how you got that particular number, instead of just presenting the final answer.
    – MisterRiemann
    Nov 24 at 15:00






  • 1




    Be careful. TECHNOLOGY has ten letters, so you have a block of three letters and seven other letters to arrange.
    – N. F. Taussig
    Nov 24 at 15:04















up vote
0
down vote

favorite












Given TECHNOLOGY , find number of distinguishable ways the letters can be arranged in which letters T,E and N are together



This is my working-



$3! cdot frac{7!}{2!} $



is this correct ?










share|cite|improve this question













put on hold as off-topic by Rushabh Mehta, MisterRiemann, NCh, Shailesh, John B Dec 1 at 0:45


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." – Rushabh Mehta, MisterRiemann, NCh, Shailesh

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









  • 5




    Solutions to such exercises should usually be presented in such a way that one can understand how you reached the answer, i.e. you should explain how you got that particular number, instead of just presenting the final answer.
    – MisterRiemann
    Nov 24 at 15:00






  • 1




    Be careful. TECHNOLOGY has ten letters, so you have a block of three letters and seven other letters to arrange.
    – N. F. Taussig
    Nov 24 at 15:04













up vote
0
down vote

favorite









up vote
0
down vote

favorite











Given TECHNOLOGY , find number of distinguishable ways the letters can be arranged in which letters T,E and N are together



This is my working-



$3! cdot frac{7!}{2!} $



is this correct ?










share|cite|improve this question













Given TECHNOLOGY , find number of distinguishable ways the letters can be arranged in which letters T,E and N are together



This is my working-



$3! cdot frac{7!}{2!} $



is this correct ?







combinatorics






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asked Nov 24 at 14:55









mutu mumu

324




324




put on hold as off-topic by Rushabh Mehta, MisterRiemann, NCh, Shailesh, John B Dec 1 at 0:45


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." – Rushabh Mehta, MisterRiemann, NCh, Shailesh

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




put on hold as off-topic by Rushabh Mehta, MisterRiemann, NCh, Shailesh, John B Dec 1 at 0:45


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." – Rushabh Mehta, MisterRiemann, NCh, Shailesh

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








  • 5




    Solutions to such exercises should usually be presented in such a way that one can understand how you reached the answer, i.e. you should explain how you got that particular number, instead of just presenting the final answer.
    – MisterRiemann
    Nov 24 at 15:00






  • 1




    Be careful. TECHNOLOGY has ten letters, so you have a block of three letters and seven other letters to arrange.
    – N. F. Taussig
    Nov 24 at 15:04














  • 5




    Solutions to such exercises should usually be presented in such a way that one can understand how you reached the answer, i.e. you should explain how you got that particular number, instead of just presenting the final answer.
    – MisterRiemann
    Nov 24 at 15:00






  • 1




    Be careful. TECHNOLOGY has ten letters, so you have a block of three letters and seven other letters to arrange.
    – N. F. Taussig
    Nov 24 at 15:04








5




5




Solutions to such exercises should usually be presented in such a way that one can understand how you reached the answer, i.e. you should explain how you got that particular number, instead of just presenting the final answer.
– MisterRiemann
Nov 24 at 15:00




Solutions to such exercises should usually be presented in such a way that one can understand how you reached the answer, i.e. you should explain how you got that particular number, instead of just presenting the final answer.
– MisterRiemann
Nov 24 at 15:00




1




1




Be careful. TECHNOLOGY has ten letters, so you have a block of three letters and seven other letters to arrange.
– N. F. Taussig
Nov 24 at 15:04




Be careful. TECHNOLOGY has ten letters, so you have a block of three letters and seven other letters to arrange.
– N. F. Taussig
Nov 24 at 15:04










3 Answers
3






active

oldest

votes

















up vote
1
down vote













I won't give the exact answer as then I'm unsure of the answer's helpfulness for other counting-type questions, but I hope that asking the following questions will lead you to the correct answer:




  • Can you explain your working for getting the 7!, 3! and 2! ?

  • Will using 7! include the possibilities where T, E, N are together but are located elsewhere?

  • In how many positions can the group of three letters be placed together?

  • Does using 7! account for all of these positions?


Perhaps these questions will lead you to the correct solution.






share|cite|improve this answer




























    up vote
    1
    down vote













    Consider $text{TEN}$ together as a block and all other letters as single block. Then you have $8$ blocks. So there are $8!$ permutations possible and $3!$ permutations of $TEN$. Also the letter $text{O}$ is not distinguishable.



    So total number of ways is $dfrac{8!cdot 3!}{2!}$.






    share|cite|improve this answer























    • @N.F.Taussig: Sorry. My bad.
      – Yadati Kiran
      Nov 24 at 16:07


















    up vote
    1
    down vote













    Assume $T,E, N $ as single letter therefore, total number of letters in the word technology is 8 this can be arranged in $8!$ ways and number of ways in which $T,E, N$ can be arranged $3!$ ways and since $O$ is repeating two times hence answer is $frac{8!×3!}{2!}$.






    share|cite|improve this answer




























      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes








      up vote
      1
      down vote













      I won't give the exact answer as then I'm unsure of the answer's helpfulness for other counting-type questions, but I hope that asking the following questions will lead you to the correct answer:




      • Can you explain your working for getting the 7!, 3! and 2! ?

      • Will using 7! include the possibilities where T, E, N are together but are located elsewhere?

      • In how many positions can the group of three letters be placed together?

      • Does using 7! account for all of these positions?


      Perhaps these questions will lead you to the correct solution.






      share|cite|improve this answer

























        up vote
        1
        down vote













        I won't give the exact answer as then I'm unsure of the answer's helpfulness for other counting-type questions, but I hope that asking the following questions will lead you to the correct answer:




        • Can you explain your working for getting the 7!, 3! and 2! ?

        • Will using 7! include the possibilities where T, E, N are together but are located elsewhere?

        • In how many positions can the group of three letters be placed together?

        • Does using 7! account for all of these positions?


        Perhaps these questions will lead you to the correct solution.






        share|cite|improve this answer























          up vote
          1
          down vote










          up vote
          1
          down vote









          I won't give the exact answer as then I'm unsure of the answer's helpfulness for other counting-type questions, but I hope that asking the following questions will lead you to the correct answer:




          • Can you explain your working for getting the 7!, 3! and 2! ?

          • Will using 7! include the possibilities where T, E, N are together but are located elsewhere?

          • In how many positions can the group of three letters be placed together?

          • Does using 7! account for all of these positions?


          Perhaps these questions will lead you to the correct solution.






          share|cite|improve this answer












          I won't give the exact answer as then I'm unsure of the answer's helpfulness for other counting-type questions, but I hope that asking the following questions will lead you to the correct answer:




          • Can you explain your working for getting the 7!, 3! and 2! ?

          • Will using 7! include the possibilities where T, E, N are together but are located elsewhere?

          • In how many positions can the group of three letters be placed together?

          • Does using 7! account for all of these positions?


          Perhaps these questions will lead you to the correct solution.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Nov 24 at 15:15









          Danila Kurganov

          112




          112






















              up vote
              1
              down vote













              Consider $text{TEN}$ together as a block and all other letters as single block. Then you have $8$ blocks. So there are $8!$ permutations possible and $3!$ permutations of $TEN$. Also the letter $text{O}$ is not distinguishable.



              So total number of ways is $dfrac{8!cdot 3!}{2!}$.






              share|cite|improve this answer























              • @N.F.Taussig: Sorry. My bad.
                – Yadati Kiran
                Nov 24 at 16:07















              up vote
              1
              down vote













              Consider $text{TEN}$ together as a block and all other letters as single block. Then you have $8$ blocks. So there are $8!$ permutations possible and $3!$ permutations of $TEN$. Also the letter $text{O}$ is not distinguishable.



              So total number of ways is $dfrac{8!cdot 3!}{2!}$.






              share|cite|improve this answer























              • @N.F.Taussig: Sorry. My bad.
                – Yadati Kiran
                Nov 24 at 16:07













              up vote
              1
              down vote










              up vote
              1
              down vote









              Consider $text{TEN}$ together as a block and all other letters as single block. Then you have $8$ blocks. So there are $8!$ permutations possible and $3!$ permutations of $TEN$. Also the letter $text{O}$ is not distinguishable.



              So total number of ways is $dfrac{8!cdot 3!}{2!}$.






              share|cite|improve this answer














              Consider $text{TEN}$ together as a block and all other letters as single block. Then you have $8$ blocks. So there are $8!$ permutations possible and $3!$ permutations of $TEN$. Also the letter $text{O}$ is not distinguishable.



              So total number of ways is $dfrac{8!cdot 3!}{2!}$.







              share|cite|improve this answer














              share|cite|improve this answer



              share|cite|improve this answer








              edited Nov 24 at 16:09

























              answered Nov 24 at 15:48









              Yadati Kiran

              1,243417




              1,243417












              • @N.F.Taussig: Sorry. My bad.
                – Yadati Kiran
                Nov 24 at 16:07


















              • @N.F.Taussig: Sorry. My bad.
                – Yadati Kiran
                Nov 24 at 16:07
















              @N.F.Taussig: Sorry. My bad.
              – Yadati Kiran
              Nov 24 at 16:07




              @N.F.Taussig: Sorry. My bad.
              – Yadati Kiran
              Nov 24 at 16:07










              up vote
              1
              down vote













              Assume $T,E, N $ as single letter therefore, total number of letters in the word technology is 8 this can be arranged in $8!$ ways and number of ways in which $T,E, N$ can be arranged $3!$ ways and since $O$ is repeating two times hence answer is $frac{8!×3!}{2!}$.






              share|cite|improve this answer

























                up vote
                1
                down vote













                Assume $T,E, N $ as single letter therefore, total number of letters in the word technology is 8 this can be arranged in $8!$ ways and number of ways in which $T,E, N$ can be arranged $3!$ ways and since $O$ is repeating two times hence answer is $frac{8!×3!}{2!}$.






                share|cite|improve this answer























                  up vote
                  1
                  down vote










                  up vote
                  1
                  down vote









                  Assume $T,E, N $ as single letter therefore, total number of letters in the word technology is 8 this can be arranged in $8!$ ways and number of ways in which $T,E, N$ can be arranged $3!$ ways and since $O$ is repeating two times hence answer is $frac{8!×3!}{2!}$.






                  share|cite|improve this answer












                  Assume $T,E, N $ as single letter therefore, total number of letters in the word technology is 8 this can be arranged in $8!$ ways and number of ways in which $T,E, N$ can be arranged $3!$ ways and since $O$ is repeating two times hence answer is $frac{8!×3!}{2!}$.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Nov 24 at 16:52









                  priyanka kumari

                  1177




                  1177















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