For questions 5 - 6, use the permutations and combinations formulas to solve the problems. 5. There are 12 people on a basketball team. The coach chooses 3 players to stay after practice and clean up. The order in which they are chosen does not matter. How many ways can the players be chosen? 6. There are 12 people on a basketball team. The coach chooses 3 players to play three different positions. How many ways can the players be chosen? Use this scenario for questions 7 - 8: You and your friend enter a drawing with 5 different prizes. The prizes are awarded randomly. A total of 15 people enter the drawing. 7. How many ways can you win first prize and your friend win second prize? 8. What is the probability that you win first prize and your friend wins second prize? Hint: Find the number of ways to award 5 prizes to 15 people. Then divide your answer to question 7 by this number. Use this scenario for questions 9 - 10: At a game show, there are 12 people (including you and your friend) in the front row. The host chooses 4 people at random from the front row to be contestants. The order in which they are chosen does not matter. 9. How many ways can you and your friend both be chosen? 10. What is the probability that you and your friend are both chosen as contestants? Hint: Find the number of ways to choose 4 people out of 12 when order does not matter. Then divide your answer to question 9 by this number