prata wrote: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?
1. 12
2. 15
3. 18
4. 24
5. 27
Since this is a 5 digit palindrome, the middle number would act like a mirror.
Case 1: Middle number = 1
_ _ 1 _ _
Number of options for 1st place = 3
Number of options for 2nd place = 3
Number of options for 4th and 5th place = 1
Total ways = 3*3 = 9
Case 2: Middle number = 2
_ _ 2 _ _
Similar to the above reasoning,
Total ways = 3*3 = 9
Case 3: Middle number = 3
_ _ 3 _ _
Similar to the above reasoning,
Total ways = 3*3 = 9
Total number of ways = 9 + 9 + 9 = 27
Correct Option:
E
