(a) I have 8 chocolates, which are indistinguishable. 5 are full of delicious caramel, while 3 have been tampered with by my assistant, Phil, and instead contain garlic puree. I begin to eat the chocolates one by one. If I eat all 5 caramel chocolates, I will stop because I am satisfied. If I eat all 3 garlic chocolates, I will stop because I feel sick. What is the probability that I stop because I feel sick?

(b) I am handing out marked homeworks to my class. Thirteen students have remembered to put their names on their homeworks, but seven have not. I therefore hand the seven unnamed homeworks at random to the seven students who forgot to add their names. What is the probability that at least five students receive the correct homework?