Congratulations! You and two of your friends are now proud owners of brand-new library cards. In order to use your new cards, all you and your friends need to do is create four-digit PINs, with numbers \(0\) - \(9\) available (in theory) at each position. Predictably, all of you have different ideas of what an acceptable PIN is (odd or even, leading zeros or not, etc.).

  1. You are fairly chill about what you want in a PIN – all you want is an even PIN, and you’re totally fine if it starts with a zero. How many possible PINs fit your preference?
  2. One of your friends is a bit more persnickety – they want a PIN divisible by \(5\), and they cannot stand PINs starting with a zero. How many possible PINs fit this friend’s preferences?
  3. Your other friend has some more…particular preferences – they have an affinity for the number \(16\) and thus want the digits \(1\) and \(6\) to appear in that exact order at some point in the PIN. Further, they also despise PINs starting with a zero. How many possible PINs fit this friend’s preferences?