A palindrome is a number that reads the same forward and backward. For example, 3663 and 23232 are palindromes. If 7-digit palindromes are formed using one or more of the digits 5, 6 and 0, how many such palindromes are possible?
A. 16
B. 54
C. 81
D. 486
E. 729
Given: A palindrome is a number that reads the same forward and backward. For example, 3663 and 23232 are palindromes. If 7-digit palindromes are formed using one or more of the digits 5, 6 and 0.
Asked: How many such palindromes are possible?
__ __ __ ___ __ __ __ __
For 1st digit, 2 choices 5 & 6 are available
For 2nd digit, 3 choices 5,6 & 0 are available
For 3rd digit, 3 choices 5,6 & 0 are available
For 4th digit, 3 choices 5,6 & 0 are available
For 5th digit, only 1 choice is available
For 6th digit, only 1 choice is available
For 7th digit, only 1 choice is available
Total number of palindromes = 2*3*3*3*1*1*1 = 54
IMO B
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com