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
Monzur R.
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" = 26xx26xx26xx1xx1=17,576#

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