I have been practising my probability skills and found a problem I wasn't able to solve. I would appreciate some help:
You have 20 horses. You randomly grab 5 of them, mark them and set them free. Later, you grab 4 of the total of horses and want to know what is the probability of the event ''exactly two of the horses you grabbed are marked'' ? The problem specifically says that you should solve it without using permutations and combinations.
I know it may be a silly problem, but I can't solve it. Thank you in advance for any help provided.