Suppose that 10 fish are caught at a lake that contains 5 distinct types of fish.
How many different outcomes are possible, where an outcome specifies the numbers of caught fish of each of the 5 types?
How many outcomes are possible when 3 of the 10 fish caught are trout?
How many when at least 2 of the 10 are trout?
Any help is greatly appreciated. I want to find out how to do this without simply using brute force. I came to an answer of 555 for the first question using brute force, but I'm not certain that's correct.