1. there are 4 candidates for a literature scholarship, 6 for political science, and 5 for economics. in how many ways can these scholarships be awarded? a. 120 b. 95 c. 115 d. 110 e. 100 2. if a fair coin is flipped 5 times, calculate the number of different outcomes in which the last coin flip is heads. a. 12 b. 10 c. 14 d. 8 e. 16 3. a class has 25 boys and 18 girls. the teacher wants to select 1 boy and 1 girl to represent the class in a function. how many ways can the teacher make the decision? a. 380 b. 450 c. 400 d. 430 e. 410 a restaurant has 240 options on the menu for pizza. each option contains exactly one type of vegetable, one type of meat, and one type of cheese. if there are 5 bread types and 8 cheeses available, how many meat options are there? 4. a. 4 b. 7 d. 8 e. 6

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)