Solve full answers
Show reasoning and all work/calculation, where possible Use proper notation (probability, combinations, permutations, etc.) For probability problems, use exact values, or reduce fractions to lowest terms 1. Jeremy decides to roll a die and toss a coin. a) Make a tree diagram or use listing / exhaustion to show the possible outcomes. b) How many different outcomes are there? 2. There are 10 councillors and 12 planning department staff available to serve on a ommittee to look into re-establishing two way traffic on the streets of St. Catharines. If the committee will consist of 3 councillors and either 1 or 2 planning staff, how many different committees could the council choose? 3. Nine stuffed animals, all different, are placed along a babies toy shelf. How many possible arrangements are there if: a) there are no restrictions. b) Cookie Monster must be in the middle c) BERT and ERNIE st be together. d) BERT, ERNIE, and OSCAR must be together. BERT, ERNIE, and OSCAR must not be together. () they must not be in alphabetical order. 4. Miss Morrison has a test bank of multiple-choice questions. 15 questions are combinations, and 12 are permutations. Miss Morrison is writing a test with 12 multiple choice questions. a) How many different tests can she write if she wants to choose 7 combination and 5 permutation multiple choice questions. b) After she has chosen the 12 questions, In how many orders can she put them on the test? 5. How many different pizza's can be ordered if the restaurant offers 15 different toppings and there is not limit to the number of toppings on the pizza? 6. 6 Teachers and 12 students volunteer for a committee to discuss extra-curricular activities. How many committees of 5 people can be made if: a) there are no restrictions b) there must be 3 students on the committee c) there must be no more than 2 teachers on the committee d) there must be at least one teacher and at least one student on the committee e) Barry and Miss Morrison cannot be on the committee together MDM4U 7. A 9-passenger van shuttles athletes between venues at the Canada Summer Games. If 22 athletes need to get to the track and field stadium, in how many ways can passengers be chosen for a) the bus's first trip? b) the bus's second trip? 8. The starting line up for a basketball team is to consist of two forwards and three guards. Two brothers are on the team. Matthew is a forward and Tony a guard. There are four forwards and six guards from which to choose the line up. If the starting players are chosen at random, what is the probability that the two brothers will end up in the starting line up? 9. In a truck meet, five entrants of equal ability are competing. What is the probability that a) the finish will be in the descending order of the entrants' ages? b) Sandy will be first? c) Shanaze is the first and Sandy is second? 10. Find the number of paths through the below grid. START END
