A group of 5 boys and 10 girls is lined up in random order -- that is, each of the 15! permutations is assumed to be equally likely.
What is the probability that the person in the 4th position is a boy?
What is the probability that a particular boy is in the 3rd position?
I don't really know how to reason about problems like this. I feel like the answer to part 1 is 14!*5. I can select one of 5 boys in the fourth position and then I have 14 people left to arrange in the remaining spots. My best guess part 2 is just 14! where one position is occupied by a particular boy and the rest of the 14 people are then arranged in the spots.
I don't understand how to think about these types of problems and I have this constant, nagging feeling of something important being left out from my reasoning.