Fishing and Probability
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 Nebagamon 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.