Counting and Probability: Word Problems

Bertie Bott also produces Bertie Bott's Every Flavor Pez. Each package contains $6$ peppermint, $2$ kumquat, $3$ chilli pepper, and $5$ garlic flavored candies in a random order. Harold opens a package and slips it into his Dumbeldore-shaped Pez dispenser. Harold then randomly dispenses $4$ candies. What is the probability that at least $3$ of these candies are garlic flavored?

Source: Lexington Math Tournament