A number is called a palindrome if it reads the same backward as well as forward. For example 285582 is a six digit palindrome. The number of six digit palindromes, which are divisible by 55 , is ____

Question

A number is called a palindrome if it reads the same backward as well as forward. For example 285582 is a six digit palindrome. The number of six digit palindromes, which are divisible by 55 , is ________.

TestHub · Accepted Answer

Palindrome Numbers only in this form will be divisible by $55$ .
Numbers can be between $0 - 9$
Number of ways of selecting value of $a = {}_{1}^{10}P$
Similarly number of ways of choosing value of $b = {}_{1}^{10}P$ (As a and b can also be same)
Therefore, Total number of ways of getting palindrome numbers divisible by $55$ is $= 1 \times 10 \times 10 \times 1 = 100$

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