I have a question about this problem that I am trying to figure out:
A string of letters is called a palindrome, if reading the string from left to right gives the same result as reading the string from right to left. For example, madam and racecar are palindromes. Recall that there are five vowels in the English alphabet: a, e, i, o, and u.
In this question, we consider strings consisting of 28 characters, with each character being a lowercase letter. Determine the number of such strings that
(i) start and end with the same letter, or
(ii) are palindromes, or
(iii) contain vowels only.
My answer so far:
$A = 26^{27}$,
$B = 26^{14}$,
$C = 5^{28}$
My question is, would I have to use a sum rule here or inclusion-exclusion rule? I am not sure about which method to use here. Any help would be appreciated.