A hardware kit contains $40$ bolts: $25$ stainless, $10$ brass, and $5$ aluminum. Two bolts are chosen at random without replacement. What is the probability that both are stainless? Give your answer as a simplified fraction.

In a class of $20$ students, $7$ students scored above the threshold on a test. Three students are chosen at random without order. What is the probability that exactly two of the chosen students scored above the threshold?

A researcher selects a random sample of $15$ university students and records each student's final exam score as a number out of $100$. Is this a binomial experiment?