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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

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Answer:

27 Palindromes are possible in the given situation.

Step-by-step 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

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