Consider the word ROTOR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5-letter palindromes ?

Options are:
A) 17756 B) 17576
C) 12657 D) 12666

1 Answer
Feb 28, 2018

The answer is B

Explanation:

A word is a palindrome if the 4th letter matches the 2nd and the fifth letter matches the 1st, and the 3rd letter can be chosen freely.

Since there are 26 letters in the alphabet, we have 26 choices for the first letter, 26 for the second and 26 for the third. Given that the fourth and fifth have to match the first and second letters respectively, we have only 1 choice for those letters.

So

Total no. of 5-letter palindromes=26×26×26×1×1=17,576