Question:
Using the ordinary alphabet and allowing repeated letters, find the number of words of length 8 that begin and end with T.
for the first letter, we have only one choice, it has to be T.
we have 26 choices for the second letter, since we can repeat. we also have 26 choices for the third letter, the fourth letter, and so on. thus the number of choices we have for words is:
$\displaystyle (1)(26)^7 = 26^7$