> 
> In this question, we consider strings consisting of 26 characters, with each character being a uppercase letter. Determine the number of such strings that  
>  
>  (a) start and end with the same letter, or  
>  
>  (b) are palindromes, or  
>  
>  (c) contain vowels only
> 
> 
> 

For this problem, I approached each scenario a, b, c separately. I then joined the 3 with an OR to satisfy the question in the final answer.

a. $26$ characters, if the last letter must be the same as the first, we really only have $25$ characters to choose from, so part a = $26^ {25}$

b. $26$ characters, but if it is a palindrome, the length is cut in half, giving us $26^{13}$. 

c. If the characters are vowels only, there are only A E I O U, $5$ characters to choose from. And we have a full 26 characters to pick. $26^{5}$

The three value then gets OR'd together

$26^ {25}$ OR $26^{13}$ OR $26^{5}$ 

Is what I did correct? I'm working from practice problems and am not given an answer key so it's hard to really practice when I don't know if I'm doing it right or wrong. Thank you!