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Magazine Problem 34
You want to purchase vegetable dip for a party. A grocery store sells 7 different flavors of vegetable dip. You have enough money to purchase 2 flavors. How many combinations of 2 flavors of vegetable dip are possible?
Problem 37
In Exercises 37-40, tell whether the question can be answered using permutations or combinations. Explain your reasoning. Then answer the question. To complete an exam, you must answer 8 questions from a list of 10 questions. In how many ways can you complete the exam?
Problem 39
Tell whether the question can be answered using permutations or combinations. Explain your reasoning. Then answer the question. Fifty-two athletes are competing in a bicycle race. How many orders can the bicyclists finish first, second, and third? (Assume there are no ties.)
Problem 40
Tell whether the question can be answered using permutations or combinations. Explain your reasoning. Then answer the question. An employee at a pet store needs to catch 5 tetras in an aquarium containing 27 tetras. In how many groupings can the employee capture 5 tetras?
Problem 43
Consider a set of 4 objects. a. Are there more permutations of all 4 of the objects or of 3 of the objects? Explain your reasoning. b. Are there more combinations of all 4 of the objects or of 3 of the objects? Explain your reasoning. c. Compare your answers to parts (a) and (b).
Problem 47
You and your friend are in the studio audience on a television game show. From an audience of 300 people, 2 people are randomly selected as contestants. What is the probability that you and your friend are chosen?
Problem 48
You work 5 evenings each week at a bookstore. Your supervisor assigns you 5 evenings at random from the 7 possibilities. What is the probability that your schedule does not include working on the weekend?
Problem 50
Find the probability of winning a lottery using the given rules. Assume that lottery numbers are selected at random. You must correctly select 4 numbers, each an integer from 0 to 9 . The order is important.
Problem 53
Use the Binomial Theorem to write the binomial expansion. \((a+3 b)^4\)
Problem 55
Use the Binomial Theorem to write the binomial expansion. \(\left(w^3-3\right)^4\)
