Final answer:
To find the number of 7-letter palindromes, we start by selecting the middle letter, then consider the remaining 6 letters. The number of 7-letter palindromes is 26^6/2.
Step-by-step explanation:
A palindrome is a word or phrase that reads the same forwards and backwards. To find the number of 7-letter palindromes, we can start by selecting the middle letter of the palindrome. Since there are 26 letters in the alphabet, we have 26 choices for the middle letter. The remaining 6 letters can be any letter, giving us 26^6 possible combinations. However, because a palindrome is the same forwards and backwards, we only need to consider half of these combinations. Therefore, the number of 7-letter palindromes is 26^6/2.