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In Exercises 1-4, does the problem involve permutations or combinations? Explain your answer. (It is not necessary to solve the problem.) A medical researcher needs 6 people to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, in how many ways can 6 people be selected?

A restaurant offers eight appetizers and ten main courses. In how many ways can a person order a two-course meal?

In Exercises 1-2, the numbers that each pointer can land on and their respective probabilities are shown. Compute the expected value for the number on which each pointer lands. $$ \begin{array}{|c|c|} \hline \text { Outcome } & \text { Probability } \\ \hline 1 & \frac{1}{2} \\ \hline 2 & \frac{1}{4} \\ \hline 3 & \frac{1}{4} \\ \hline \end{array} $$

In Exercises 1-6, you are dealt one card from a 52-card deck. Find the probability that you are not dealt an ace.

The model of the car you are thinking of buying is available in nine different colors and three different styles (hatchback, sedan, or station wagon). In how many ways can you order the car?

Three men and three women line up at a checkout counter in a store. a. In how many ways can they line up? b. In how many ways can they line up if the first person in line is a woman, and then the line alternates by genderthat is a woman, a man, a woman, a man, and so on? c. Find the probability that the first person in line is a woman and the line alternates by gender.

A popular brand of pen is available in three colors (red, green, or blue) and four writing tips (bold, medium, fine, or micro). How many different choices of pens do you have with this brand?

Six stand-up comics, A, B, C, D, E, and F, are to perform on a single evening at a comedy club. The order of performance is determined by random selection. Find the probability that a. Comic E will perform first. b. Comic \(\mathrm{C}\) will perform fifth and comic B will perform last. c. The comedians will perform in the following order: D, E, C, A, B, F. d. Comic \(\mathrm{A}\) or comic \(\mathrm{B}\) will perform first.

You are dealt one card from a 52-card deck. Find the probability that you are not dealt a heart.

In how many ways can a casting director choose a female lead and a male lead from five female actors and six male actors?