1. Question #1 A bag has 10 red, 3 yellow, and 5 blue marbles. You pick one. What is the probability that you select a blue marble?

2. Answer #1

3. Question #2 A card is chosen at random from a standard deck of 52 cards. What is the probability that you select a jack?

4. Answer #2

5. Question #3 You have 10 packages of M&Ms and 15 packages of Skittles. In how many ways can you pick 8 and have 3 be M&Ms?

6. Answer #3 360360 (10C3*15C5)

7. Question #4 In how many ways can you line up the letters in the word “REARRANGE”

8. Answer #4 15120 Work: 9!/(2!2!3!)

9. Question #5 A password consists of 3 digits, repetition is not allowed, followed by 2 letters, repetition is allowed. What is the total number of possible passwords?

10. Answer #5 486,720 Work 10*9*8*26*26

11. Question #6 A card is chosen at random from a standard deck of 52 cards. What is the probability that you select a jack, queen, king, OR ace?

12. Answer #6

13. Question #7 Forty students apply for a scholarship awarded by the headmaster. One is for $5000, one is for $1000, and the last is for $500. In how many ways can the recipients be selected?

14. Answer #7 59280 Work: 40P3 or 40*39*38

15. Question #8 In how many ways can ten students from a class of twenty line up?

16. Answer #8 About 6.7x10^11 20P10 or 20*19*18…11

17. Question #9 You are ordering a new bike. You have 5 wheel choices, 3 color choices and 2 seat choices. How many possible bikes can you design?

18. Answer #9 30 Work: 5*3*2

19. Question #10 In how many ways can a committee of 4 students be selected from a pool of 7 students?

20. Answer #10

21. Question # 11 In how many ways can you arrange six items on a circular display?

22. Answer #11 120 Work: 5! Or 6!/6

23. Question #12 In how many ways can the batting order for the 9 starting players be announced?

24. Answer #12 362880 Work: 9! Or 9P9

25. Question #13 DS Pizza Shop offers 4 different cheeses and 10 different pizza toppings. How many ways can you order a pizza with 1 type of cheese and 2 different toppings?

26. Answer #13 180 Work: 4C1*10C2

27. Question #14 In how many ways can 3 males and 3 females be seated in a line if gender must alternate?

28. Answer #14 72 If start male: 3*3*2*2*1*1 If start female: 3*3*2*2*1*1 Add options together

29. Question #15 A bag contains 8 blue marbles and 4 red marbles. What is the probability of picking exactly 3 red if you are selecting five marbles from the bag?

30. Answer #15

31. Question #16 Five different mathematics textbooks are being arranged on a student’s desk. How many different arrangements are possible?

32. Answer #16 120

33. Question #17 A man has 5 shirts and 3 ties in his suitcase. How many different shirt and tie combinations can he wear?

34. Answer #17 15

35. Question #18 How many different four digit codes are possible if the first digit can not be 0 and repeated digits are allowed?

36. Answer #18 9000

37. Question #19 If 4 people enter a bus (one at a time) having 9 vacant seats, in how many ways can they be seated?

38. Answer #19 3024 9*8*7*6

39. Question #20 How many different arrangements are there of the letters in the word ROSE?

40. Answer #20 24

41. Question #21 Companies whose stock are listed on the New York Stock Exchange have their company name represented by either 1, 2, OR 3 letters (repetition of letters is allowed). What is the maximum number of companies that can be listed on the NYSE? Hint: One letter codes + Two letter codes + Three letters codes

42. Answer #21 18,278 (26+676+17576)

43. Question #22 The United Nations Security Council has 15 member nations. In how many ways can the representatives be seated around a circular table if each nation has one representative?

44. Answer #22 14!

45. Question #23 How many different vertical arrangements are there of 10 flags if 4 are white, 3 are blue, 2 are red, and 1 is green?

46. Answer #23 12,600

47. Question #24 A take-out restaurant offers a selection of 5 main dishes, 4 vegetables, and 3 desserts. In how many ways can a family chose a meal that consists of 2 main dishes, 3 different vegetables, and 1 dessert?

48. Answer #24 120

49. Question #25

50. Answer #25