Question 1

a) When choosing activities at college, Mary wants to try an intramural sport and a club. There are 5 intramural teams and 20 clubs offered in the fall. If Mary chooses one from each category, how many choices does she have?

b) When planting a garden, you can choose from three types of tomatoes, four types of peppers, and two types of squash. If you choose only one crop from each category, how many possible garden combinations can you make?

c) When selecting your schedule in school, you can choose from three math courses, four English courses, three science courses, and two history courses. How many choices do you have for your schedule if you need to select one math, one English, one science, and one history course?

d) You have room in your schedule for one more class. There are six elective courses to choose from. How many choices of schedules do you now have?

e) In a survey on favorite parts of college, students were asked to choose their favorite professor (from a list of four popular professors), favorite meal in the dining hall (from a list of six popular meals), and favorite weekend activity (from a list of seven popular activities). Calculate the number of different ways the survey can be filled out if students select one from each category.

f) What is the probability that a student who chose his or her selections totally at random chose the third one on each list? (Enter your probability as a fraction.)

g) After compiling the results from the survey described above, a follow-up survey is written with the top two in each category (top two professors, top two meals, and top two activities). Calculate the number of different ways the survey can be filled out if students select one from each category.