Question

A palindrome is a number that reads the same forward and backward. For example. 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits, 1, 2, 3, how many such palindromes are possible?A) 12B) 15C) 18D) 24E) 27

Answer 1

(E) 27

Explanation:

Let the 5 digit palindrome be PQRQP

Since each digit is chosen from 1,2,3 therefore

P can either be 1,2 or 3 which gives us 3 options.

Q can also either be 1,2 or 3 which gives us 3 options

R can either be 1,2 or 3 which also gives us 3 options

So we have 3^3 = 3*3*3

= 27

This means 27 palindromes are possible if they are formed using one or more of the digits, 1, 2, 3.