1. Twelve individuals want to form a committee of four.
(a.) How many committees are possible?
(b.) The 12 individuals consist of 5 biologists, 4 chemists, and 3 physicists. How many committees consisting of 1 biologist, 1 chemist, and 2 physicists are possible?
(c.) In the setting of part (b), if all committees are equally as likely, what is the probability the committee formed will consist of 1 biologist, 1 chemist, and 2 physicists?
2. You are out of town at a research conference; in your suitcase, you have two white shirts, 3 black shirts, 2 pairs of black slacks, and 3 pairs of gray slacks. What is the likelihood you wear an all-black outfit?
3. In many states, the license plates consist of a string of seven characters such that the first three are letters and the second four are numbers. Assume each string of characters are equally as likely and repetition is allowed on a single license plate.
(A.) Describe the random variable,X, that counts the number of vowels in each license plate. (Do not consider y as a vowel.)
(b) Give the probability mass function, p(x) , for this scenario.
(c) Use it to find the likelihood a license plate will have three vowels.
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