I cannot understand why T A T A T A has 6 members.  Is there always
6 members taken from the 4 members {A,G,T,C}?  Why 4 letters to choose
from and 6 to choose?

If so, we want this   

 

And since "AND" tells us to multiply probabilities:

 

    

I am not sure what you mean by the second part?  Are there always 6 letters,
as in T A T A T A?  Or are there sometimes only four, like T A T A, and
sometimes 7 or 8 like T A T A T A T, or T A T A T A T A, and sometimes even
only 2 like T A??  

If you will explain whether there are always 6 letters, as in  in T A T A T A
or if there can be other numbers of them besides 6 in the thank-you note, I'll
get back to= you and help you with the 2nd part. (free of charge, of course.)

Edwin