How many three digits even numbers can we form such that if one of digit is $5$ the following digit must be $ 7$?

How many three digits even numbers can we form such that if one of digit is $5$ the following digit must be $ 7$?

I need some ideas on how to proceed on this problem.


You have two different kinds of such three-digit even numbers.

  • $57x$, where $x$ can only be $0,2,4,6,8$ which is just $5$ possibilities.

  • For the remaining, you count all even three-digit numbers with no $5$ in them. This will be $8\times 9\times 5 = 360$

So you have $365$ possibilities.