Last week, Pat caught n distinct fish from Lake Nebagamon, but threw all of them back at the end of the fishing trip. Next week, Pat will go fishing again at the same place, and this time will catch k fish without throwing any back. Lake Nebagmon will contain a total of f fish next week. Assuming that Pat catches fish at random, and that no fish die or are removed from the lake between last week and next week, find the probability that exactly m of the fish that Pat will catch next week are fish that Pat also caught last week. I'm just wondering if I can solve this problem by using permutations and the counting principle, or if there's another advanced way of going about this that I'm not seeing at the moment. Thanks!