How many double letter mutations are possible in a certain DNA string?

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We are currently doing permutations and factorials in my Maths course. In this week's online quiz there's a question that goes like this:




A DNA sequence can be represented as a string of the letters ACTG. Given a DNA sequence of length 26, how many double letter mutations are possible?




I have absolutely no background in Chemistry or Genetics so I think I'm interpreting the question incorrectly. Here's what I've tried:



  • Picking two random positions and changing each of them: 26*3*25*3

  • Picking two adjacent positions and changing each of them: 25*3*1*3

All my attempts have been marked as incorrect by the auto-marker. Any ideas?




permutations




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  • Define 'double letter mutations' please
    – Karn Watcharasupat
    Jul 29 at 12:33










  • @KarnWatcharasupat yes that's exactly the problem. The quoted text is all information I'm given.
    – George Rautenbach
    Jul 29 at 12:38










  • Does it actually mean only two of the letters are used?
    – Karn Watcharasupat
    Jul 29 at 12:38










  • Picking two random positions is $(26)(25)/2$, not $(26)(25)$.
    – Gerry Myerson
    Jul 29 at 12:46










  • @GerryMyerson Bingo! Submit an answer and I'll mark it correct. I apologise to the rest of the community for wasting your time.
    – George Rautenbach
    Jul 29 at 12:50














up vote
1
down vote

favorite
1












We are currently doing permutations and factorials in my Maths course. In this week's online quiz there's a question that goes like this:




A DNA sequence can be represented as a string of the letters ACTG. Given a DNA sequence of length 26, how many double letter mutations are possible?




I have absolutely no background in Chemistry or Genetics so I think I'm interpreting the question incorrectly. Here's what I've tried:



  • Picking two random positions and changing each of them: 26*3*25*3

  • Picking two adjacent positions and changing each of them: 25*3*1*3

All my attempts have been marked as incorrect by the auto-marker. Any ideas?




permutations




share|cite|improve this question



















  • Define 'double letter mutations' please
    – Karn Watcharasupat
    Jul 29 at 12:33










  • @KarnWatcharasupat yes that's exactly the problem. The quoted text is all information I'm given.
    – George Rautenbach
    Jul 29 at 12:38










  • Does it actually mean only two of the letters are used?
    – Karn Watcharasupat
    Jul 29 at 12:38










  • Picking two random positions is $(26)(25)/2$, not $(26)(25)$.
    – Gerry Myerson
    Jul 29 at 12:46










  • @GerryMyerson Bingo! Submit an answer and I'll mark it correct. I apologise to the rest of the community for wasting your time.
    – George Rautenbach
    Jul 29 at 12:50












up vote
1
down vote

favorite
1









up vote
1
down vote

favorite
1






1





We are currently doing permutations and factorials in my Maths course. In this week's online quiz there's a question that goes like this:




A DNA sequence can be represented as a string of the letters ACTG. Given a DNA sequence of length 26, how many double letter mutations are possible?




I have absolutely no background in Chemistry or Genetics so I think I'm interpreting the question incorrectly. Here's what I've tried:



  • Picking two random positions and changing each of them: 26*3*25*3

  • Picking two adjacent positions and changing each of them: 25*3*1*3

All my attempts have been marked as incorrect by the auto-marker. Any ideas?




permutations




share|cite|improve this question











We are currently doing permutations and factorials in my Maths course. In this week's online quiz there's a question that goes like this:




A DNA sequence can be represented as a string of the letters ACTG. Given a DNA sequence of length 26, how many double letter mutations are possible?




I have absolutely no background in Chemistry or Genetics so I think I'm interpreting the question incorrectly. Here's what I've tried:



  • Picking two random positions and changing each of them: 26*3*25*3

  • Picking two adjacent positions and changing each of them: 25*3*1*3

All my attempts have been marked as incorrect by the auto-marker. Any ideas?





permutations





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share|cite|improve this question




share|cite|improve this question









asked Jul 29 at 12:26









George Rautenbach

172




172











  • Define 'double letter mutations' please
    – Karn Watcharasupat
    Jul 29 at 12:33










  • @KarnWatcharasupat yes that's exactly the problem. The quoted text is all information I'm given.
    – George Rautenbach
    Jul 29 at 12:38










  • Does it actually mean only two of the letters are used?
    – Karn Watcharasupat
    Jul 29 at 12:38










  • Picking two random positions is $(26)(25)/2$, not $(26)(25)$.
    – Gerry Myerson
    Jul 29 at 12:46










  • @GerryMyerson Bingo! Submit an answer and I'll mark it correct. I apologise to the rest of the community for wasting your time.
    – George Rautenbach
    Jul 29 at 12:50
















  • Define 'double letter mutations' please
    – Karn Watcharasupat
    Jul 29 at 12:33










  • @KarnWatcharasupat yes that's exactly the problem. The quoted text is all information I'm given.
    – George Rautenbach
    Jul 29 at 12:38










  • Does it actually mean only two of the letters are used?
    – Karn Watcharasupat
    Jul 29 at 12:38










  • Picking two random positions is $(26)(25)/2$, not $(26)(25)$.
    – Gerry Myerson
    Jul 29 at 12:46










  • @GerryMyerson Bingo! Submit an answer and I'll mark it correct. I apologise to the rest of the community for wasting your time.
    – George Rautenbach
    Jul 29 at 12:50















Define 'double letter mutations' please
– Karn Watcharasupat
Jul 29 at 12:33




Define 'double letter mutations' please
– Karn Watcharasupat
Jul 29 at 12:33












@KarnWatcharasupat yes that's exactly the problem. The quoted text is all information I'm given.
– George Rautenbach
Jul 29 at 12:38




@KarnWatcharasupat yes that's exactly the problem. The quoted text is all information I'm given.
– George Rautenbach
Jul 29 at 12:38












Does it actually mean only two of the letters are used?
– Karn Watcharasupat
Jul 29 at 12:38




Does it actually mean only two of the letters are used?
– Karn Watcharasupat
Jul 29 at 12:38












Picking two random positions is $(26)(25)/2$, not $(26)(25)$.
– Gerry Myerson
Jul 29 at 12:46




Picking two random positions is $(26)(25)/2$, not $(26)(25)$.
– Gerry Myerson
Jul 29 at 12:46












@GerryMyerson Bingo! Submit an answer and I'll mark it correct. I apologise to the rest of the community for wasting your time.
– George Rautenbach
Jul 29 at 12:50




@GerryMyerson Bingo! Submit an answer and I'll mark it correct. I apologise to the rest of the community for wasting your time.
– George Rautenbach
Jul 29 at 12:50










2 Answers
2






active

oldest

votes

















up vote
2
down vote



accepted










Picking two random positions is $26times25over2$, not $26times25$, so the answer they want is $$26times25over2times3times3$$






share|cite|improve this answer




























    up vote
    0
    down vote













    If double-letter mutation means only 2 of the 4 letters are used, then



    • choose 2 letters: $binom42$


    • choose the $i$ slots that would be filled by the 'first' letter: $binom26i$, $1le i le 25$


    • sum through all possible $i$'s.


    Number of mutations is
    $$binom42sum_i=1^25binom26i=6cdot67,108,862=402,653,172$$






    share|cite|improve this answer





















    • Unfortunately not the correct answer.
      – George Rautenbach
      Jul 29 at 12:47










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    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    2
    down vote



    accepted










    Picking two random positions is $26times25over2$, not $26times25$, so the answer they want is $$26times25over2times3times3$$






    share|cite|improve this answer

























      up vote
      2
      down vote



      accepted










      Picking two random positions is $26times25over2$, not $26times25$, so the answer they want is $$26times25over2times3times3$$






      share|cite|improve this answer























        up vote
        2
        down vote



        accepted







        up vote
        2
        down vote



        accepted






        Picking two random positions is $26times25over2$, not $26times25$, so the answer they want is $$26times25over2times3times3$$






        share|cite|improve this answer













        Picking two random positions is $26times25over2$, not $26times25$, so the answer they want is $$26times25over2times3times3$$







        share|cite|improve this answer













        share|cite|improve this answer



        share|cite|improve this answer











        answered Jul 29 at 12:54









        Gerry Myerson

        142k7143292




        142k7143292




















            up vote
            0
            down vote













            If double-letter mutation means only 2 of the 4 letters are used, then



            • choose 2 letters: $binom42$


            • choose the $i$ slots that would be filled by the 'first' letter: $binom26i$, $1le i le 25$


            • sum through all possible $i$'s.


            Number of mutations is
            $$binom42sum_i=1^25binom26i=6cdot67,108,862=402,653,172$$






            share|cite|improve this answer





















            • Unfortunately not the correct answer.
              – George Rautenbach
              Jul 29 at 12:47














            up vote
            0
            down vote













            If double-letter mutation means only 2 of the 4 letters are used, then



            • choose 2 letters: $binom42$


            • choose the $i$ slots that would be filled by the 'first' letter: $binom26i$, $1le i le 25$


            • sum through all possible $i$'s.


            Number of mutations is
            $$binom42sum_i=1^25binom26i=6cdot67,108,862=402,653,172$$






            share|cite|improve this answer





















            • Unfortunately not the correct answer.
              – George Rautenbach
              Jul 29 at 12:47












            up vote
            0
            down vote










            up vote
            0
            down vote









            If double-letter mutation means only 2 of the 4 letters are used, then



            • choose 2 letters: $binom42$


            • choose the $i$ slots that would be filled by the 'first' letter: $binom26i$, $1le i le 25$


            • sum through all possible $i$'s.


            Number of mutations is
            $$binom42sum_i=1^25binom26i=6cdot67,108,862=402,653,172$$






            share|cite|improve this answer













            If double-letter mutation means only 2 of the 4 letters are used, then



            • choose 2 letters: $binom42$


            • choose the $i$ slots that would be filled by the 'first' letter: $binom26i$, $1le i le 25$


            • sum through all possible $i$'s.


            Number of mutations is
            $$binom42sum_i=1^25binom26i=6cdot67,108,862=402,653,172$$







            share|cite|improve this answer













            share|cite|improve this answer



            share|cite|improve this answer











            answered Jul 29 at 12:42









            Karn Watcharasupat

            3,7992426




            3,7992426











            • Unfortunately not the correct answer.
              – George Rautenbach
              Jul 29 at 12:47
















            • Unfortunately not the correct answer.
              – George Rautenbach
              Jul 29 at 12:47















            Unfortunately not the correct answer.
            – George Rautenbach
            Jul 29 at 12:47




            Unfortunately not the correct answer.
            – George Rautenbach
            Jul 29 at 12:47












             

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