Suppose we want to choose 6 objects, without replacement, from 8 distinct objects. (If necessary, consult a list of formulas.) (a) How many ways can this be done, if the order of the choices matters? (b) How mary ways an this be done, if the order of the choices does not matter? \( \square \)

In an aquarium, there are 7 large fish and 6 small fish. Half of the small fish are red. One fish is selected at random. Find the probability that it is a small, red fish. Write your answer as a fraction in simplest form.

Probability involving one die or choosing from n distinct objects A bag contains seven tiles labeled \( B, C, D, E, F, G \), and \( H \). One tile will be randomly picked. What is the probability of picking a vowel? Write your answer as a fraction in simplest form.

Question A professor gives a surprise quiz with one multiple choice question. There are 4 answer possibilities: B, C, and D. What is the probability that you randomly guess and select the correct answer? Give your answer as a fraction.

A six-sided die with sides labeled 1 through 6 will be rolled once. Each number is equally likely to be rolled. What is the probability. of rolling a number greater than 2 ? Write your answer as a fraction in simplest form.

Question When a coin is tossed three times, what is the probability that all three tosses are heads? The possible outcomes for the coin tosses are \( \{H H H, T T T, H T T, H H T, T H H, T T H, H T H, T H T\} \) - Express your answer as a simplified fraction.