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, and 3, how many such palindromes are possible?A) 12

B) 15
C) 18
D) 24
E) 27

Answer 1

27 Palindromes are possible in the given situation.

Explanation:

As a palindrome is a number that reads the same forward and backward and in our case, it is a 5 digit palindrome.

Let's suppose the 5 digit palindrome is ABCBA:

As we know that the digits on 4th and 5th positions will be the same as the digits on 1st and 2nd positions.

1. The number of possibilities that a digit can come on 1st position are 3
2. The The number of possibilities that a digit can come on 2nd position are 3
3. The number of possibilities that a digit can come on 3rd position are 3

So the total number of possibilities that we can get 5 digit palindromes from digits 1, 2 and 3 are:

= 3 x 3 x 3

Total Palindromes = 27