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- Problem: Of 1,000 people consulted, 811 liked chocolates, 752 liked toffees and 418 liked sweets, 570 liked chocolates and toffees; 356 chocolates and sweets and 348 liked toffees and sweets : 297 liked all three. Is this information correct?A large research project is looking for more researchers. There are 8 spots open on the research team. There are 10 mathematicians and 14 computer scientists that apply for the team. a. How many different ways can a team of 8 be made for the project? b. How many different ways can a team of 8 be made for the project if the team must contain at least one computer scientist and at least one mathematician.Consider the following problem: Three officers-a president, a treasurer, and a secretary-are to be chosen from among four people: Ann, Bob, Cyd, and Dan. Suppose that, for various reasons, Ann cannot be president and either Cyd or Dan must be secretary. How many ways can the officers be chosen?
- 3. Maria and John have decided that once they live in a house, they want to have a pet. They go to an animal shelter and find several pets that they would love to take home. There are 3 Siamese cats, 3 German Shepherds, 9 Labrador Retrievers, and 22 mixed breed dogs. Since they can’t decide, they place all the adoption cards in a container and draw one. Answer each of the following questions separately, showing all your work to reach each answer. A. What is the probability that they select a cat? B. What is the probability that they select either a German Shepherd or a Labrador Retriever? C. What is the probability that if they select a dog, that it is not a mixed breed? D. What are the odds in favor of and against choosing a Siamese cat?4. Evaluate de V20 – 02Two construction companies, Giant and Sky, bid for the right to build in a field. The possible bids are $ 10 Million, $ 20 Million, $ 30 Million, S 35 Million and S 40 Million. The winner is the company with the higher bid. The two companies decide that in the case of a tie (equal bids), Giant is the winner and will get the field. Giant has ordered a survey and, based on the report from the survey, 1 concludes that getting the field for more than $ 35 Million is as bad as not getting it (assume loss), except in case of a tie (assume win) Sky is not aware of this survey. (a) State reasons why/how this game can be described as a two-players zero-sum game [
- There are 53 students. Of these, 25 are taking Business, 26 are taking English, and 25 are taking Math. 14 are taking both Business and Math, 13 are taking Math and English, and 17 are taking Business and English. 12 students are taking none of these three classes. How many students are taking Business but are not taking Math?Suppose your school has 1000 students. Why can you be pretty sure that some pair of them will have telephone numbers that end in the same two digits and that they will like the same brand of soda?