Simple Concept Tough Problem – 2

Hello readers! This is the second of a series of articles dealing with tough mathematical problems that require just basic mathematics for their solutions. A bit late, though. The first article was published on 25th October 2019. The problem for the second article is taken from the question paper of Pre-Regional Mathematics Olympiad (PRMO) 2018. I provide a solution using the concept of congruences and the basic counting principles. Here is the question (I have modified it a bit):

Consider six digit numbers of the form abccba . How many of these numbers are divisible by 7 ? If b is odd, then how many of these are divisible by 7?

Let us discuss the solution to this problem in the video below.