A new lottery has been introduced, where five balls are randomly chosen from a set numbered 1-64. Players pay $1 and choose five numbers. If they match exactly three of the numbers drawn (in any order), they win $100; if they match exactly four of the numbers drawn (in any order), they win $10,000; if they match all five of the numbers drawn (in any order), they win $1,000,000. 12. How many possible results are there from the drawing? 13. a. How many ways could a player match all five numbers? b. What is the probability of a player winning $1,000,000 (round to 8 places)? 14. a. How many ways could a player match exactly four of the five numbers? b. What is the probability of a player winning $10,000 (round to 8 places)? 15. a. How many ways could a player match exactly three of the five numbers? b. What is the probability of a player winning $100 (round to 8 places)? 16. a. How many ways could a player match fewer than three of the five numbers? b. What is the probability of a player winning nothing (round to 8 places)? 17. What is the expected value for a player buying one ticket for this lottery (round to 4 places)? 18. If one million tickets are sold, what would the lottery's expected profit be