First, note that due to multiple problems with the Episode 5 video, I had to reupload it to YouTube twice, but I believe the problem is now resolved.

During our eighth lesson together, Antonio has it easy. He has already learned many counting techniques over the previous seven lessons (probability on discrete random variables). Now he gets to practice his combinatorial chops with probability problems that require making use of those techniques. Okay, "easy" is not the right word. But it is eye opening for many students to find out how many probability problems they can work after a few weeks of practicing those methods.

Even better, Antonio told me during this lesson that he has been working on problems with a friend. There is little better way to learn math than to spend time teaching or explaining mathematical concepts to another person. That he started doing this on his own demonstrates a mindset that is helping to carry him through this journey.