# Mathematics

1. To win at LOTTO in one state, one must correctly select 6 numbers from a collection of 54 numbers (1 through 54). The order in which the selection is made does not matter. How many different selections are possible? There are ___ different LOTTO selections. 2. In how many ways can a committee of three men and three women be formed from a group of eight men and ten women? A committee of three men and three women can be formed from a group of eight men and ten women in __ different ways. 3. The Senate in a certain state is comprised of 55 Republicans, 41 Democrats, and 4 Independents. How many committees can be formed if each committee must have 3 Republicans and 2 Democrats? ____ committees can be formed. 4. You are dealt one card from a standard 52-card deck. Find the probability of being dealt a diamond. The probability of being dealt diamond is___? 5. You are dealt one card from a standard 52-card deck. Find the probability of being dealt the two of spades. The probability of being dealt the two of spades is? 6. You are dealt one card from a standard 52-card deck. Find the probability of being dealt a heart and a spade. The probability of being dealt a heart and a spade is? 7. A fair coin is tossed three times in succession. The set of equally likely outcomes is (HHH,HHT,HTH,THH,HTT,THT,TTH,TTT). Find the probability of getting exactly two heads is___? 8. A fair coin is tossed 2 times in succession. The set of equally likely outcomes is (HH, HT, TH, TT). Find the probability of getting a tail on the second toss. The probability of getting a tail on the second toss is____? 9. You select a family with three children. If M represents a male child, and F represents a female child, the set of equally likely outcomes for the childrenâ€™s genders is (MMM,MMF, MFM, MFF, FMM, FMF, FFM, FFF). Find the probability of selecting a family with fewer than 5 male children. P(fewer than 5 male children)= 10. A restaurant offers 8 appetizers and 6 main courses. In how many ways can a person order a two-coarse meal? There are ___ ways a person can order a two-coarse meal. 11. A popular brand of pen is available in 3 colors and 2 writing tips. How many different choices of pens do you have with this brand? There are ___ different choices of pens with this brand. 12. An ice cream store sells 5 drinks, in 4 sizes, and 8 flavors. In how many ways can a customer order a drink? There are ___ ways that the customer can order a drink. 13. A restaurant offers the following limited lunch menu. Main Courses Beef, Pork Roast, Duck, Quiche Vegetables Broccoli, Carrots, Potatoes Beverages Coffee, Tea, Milk, Soda Desserts Cake, Pie, Sherbet If one item is selected from each of the four groups, in how many ways can a meal be ordered? There are ___ ways a meal can be ordered. 14. A person can order a new car with a choice of 8 possible colors, with or without air conditioning, with or without automatic transmission, with or without power windows, and with or without a CD player. In how many different ways can a new car be ordered with regard to these options? There are ___ different ways that a new car can be ordered. 15. You are taking a multiple-choice test that has 7 questions. Each of the questions has 4 answer choices, with one correct answer per question. If you select one of these choices for each question and leave nothing blank, in how many ways can you answer the questions? You can answer the questions in ___ways. 16. License plates in a particular state display 3 letters followed by 2 numbers. How many different license plates can be manufactured for this state? There are ___ different license plates that can be manufactured for this state. 17. A stock can go up, go down, or stay unchanged. How many possibilities are there if you own 3 stocks? There are ___possibilities with 3 stocks. 18. A 12-sided die is rolled. The set of equally likely outcomes is (1,2,3,4,5,6,7,8,9,10,11,12). Find the probability of rolling a 7. The probability of rolling a 7 is? 19. A 12-sided die is rolled. The set of equally likely outcomes is (1,2,3,4,5,6,7,8,9,10,11,12). Find the probability of rolling a number less than 10. The probability of rolling a number less than 10 is? 20. A 12-sided die is rolled. The set of equally likely outcomes is (1,2,3,4,5,6,7,8,9,10,11,12). Find the probability of rolling a number greater than 2. The probability of rolling a number greater than 2 is? 21. A sales representative can take one of 3 different routes from City A to City E and any one of 6 different routes from City E to City M. How many different routes can she take from City A to City M, going through City E? There are ____ possible routes. 22. Simone, Tyrone, Katrina, Dawn, Ian, and Jim have all been invited to a dinner party. They arrive randomly and each person arrives at a different time. a. In how many ways can they arrive? b. In how many ways can Simone arrive first and Jim last? c. Find the probability that Simone will arrive first and Jim last? 23. A group consists of seven men and six women. Three people are selected to attend a conference. a. In how many ways can three people be selected from this group of thirteen? b. In how many ways can three women be selected from the six women? c. Find the probability that the selected group will consist of all women. 24. To play a certain lottery, a person has to correctly select 6 out of 60 numbers, paying $1 for each six-number selection. If the six numbers picked are the same as the ones drawn by the lottery, mountains of money are bestowed. a. What is the probability that a person with one combination of six numbers will win? b. What is the probability of winning if 100 different lottery tickets are purchased? 25. A box contains 26 transistors, 6 of which are defective. If 6 are selected at random, find the probability that: a. All are defective. b. None are defective. 26. A city council consists of eight Democrats and seven Republicans. If a committee of six people is selected, find the probability of selecting two Democrats and four Republicans. 27. If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability that all 4 cards are diamonds. The probability is? 28. If you are dealt 6 cards from a shuffled deck of 52 cards, find the probability of getting three queens and three kings. 29. You are dealt one card from a 52-card deck. Find the probability that you are not dealt a four. The probability is? 30. You are dealt one card from a 52-card deck. Find the probability that you are not dealt a diamond. The probability is? 31. A single die is rolled. Find the probability of rolling an odd number or a number less than 4. The probability is? 32. You are dealt one card from a 52-card deck. Find the probability that you are dealt a six or a black card. The probability is? 33. The winner of a raffle will receive a 21-foot outboard boat. If 4000 raffle tickets were sold and you purchased 30 tickets, what are the odds against your winning the boat? The odds against winning the boat are? 34. Of the 47 plays attributed to a playwright, 17 are comedies, 10 are tragedies, and 20 are histories. If one play is selected at random, find the odds in favor of selecting a comedy or a tragedy. The odds in favor are? 35. Six stand-up comics, A, B, C, D, E, and F, are to perform on a single evening at a comedy club. The order of performance is determined by random selection. Find the probability that: a. Comic E will perform fifth. b. Comic B will perform fifth and comic D will perform first. C. The comedians will perform in the following order: E, B, D, F, C, A. d. Comic C or Comic A will perform second.