Let
1. Find the following: (Putting the above information in a Venn diagram is helpful).
(each part is 3 points for 21 points)
a.
b.
c.
d.
e.
f.
g.
2. A cafeteria serves four different vegetables, five different main dishes consisting of either fish or meat, and three different deserts. If a customer chooses one serving from each of these categories, how many different combinations of vegetables, main dishes, and deserts are possible? 10 points
3. A shoe salesperson has ten different western boots to display in her showcase window. She can display only four at one time. How many different sets of four western boots can the salesperson select? 10 points
4. A school’s student union must select the officers for the current year. There are 12 representatives in the union from which a president, vice president, secretary, and treasurer will be selected. How many possible groups of officers are there? 10 points
5. A group consisting of twelve women and nine men must select a five-person committee. How many different committees are possible if it must consist of the following? 15 points
a. three women and two men
b. any mixture of men and women
6. A department store surveyed 428 shoppers, and the following information was obtained: 214 made a purchase, and 299 were satisfied with the service they received. If 52 of those who made purchase were not satisfied with the service, how many shoppers did the following? (two events problem purchase, P satisfied, S ) 15 points
a. made a purchase and were satisfied with the service
b. made a purchase or were satisfied with the service
c. were satisfied with the service but did not make a purchase
d. were not satisfied and did not make a purchase
7. Recently U2, Sting, and Lollapalooza each toured the United States. A large group of college students was surveyed, and the following information was obtained: 1533 saw U2, 1127 saw string, 581 saw Lollapalooza, 219 saw all the three, 1853 saw none, 766 saw only U2, 654 saw U2 and Sting, and 92 saw Sting and Lollapalooza but not U2. (this is a 3-event problem) 19 points
a. What percent of the college students saw all the three acts?
b. What percent of the college students saw at least two of the acts?