




Is my reasoning correct? How can I explain this in a more mathematically professional way?
I was about to post this without thinking about a possible solution, until I decided that trying to calculate every single sequence of 3! And 4! was worth the effort. I just need help with the conclusion of this problem and in case I made any mistakes. Also, I would really appreciate it if you guys could help me with presenting this reasoning in a more professional way, and if you could tell me how can I write the final formula to calculate the average number of times one checks the whole deck.