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












1














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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closed as off-topic by Don Thousand, 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." – Don Thousand, 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
















1














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













closed as off-topic by Don Thousand, 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." – Don Thousand, 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














1












1








1







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

374




374




closed as off-topic by Don Thousand, 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." – Don Thousand, MisterRiemann, NCh, Shailesh

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




closed as off-topic by Don Thousand, 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." – Don Thousand, 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


















2














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





























    1














    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





























      1














      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


















      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      2














      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


























        2














        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
























          2












          2








          2






          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

          1297




          1297























              1














              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


























                1














                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
























                  1












                  1








                  1






                  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























                      1














                      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
















                      1














                      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














                      1












                      1








                      1






                      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

                      1,684519




                      1,684519












                      • @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



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