1. In how many ways can you arrange the letters in the word 'CAT'?
2. A student has 6 different books (A, B, C, D, E, F) and wants to arrange exactly 4 of them in a row on a shelf. Since the left-to-right order matters, how many possible arrangements are there?
3. A club has 8 members. How many different ways can the club choose a president, vice-president, and secretary?
4. How many ways can you choose 2 students from a group of 8?
5. In how many ways can 5 people be seated around a circular table?
6. In a tournament, there are 5 single matches. How many ways can the matches be arranged if no match can be repeated?
7. A group of 6 friends is trying to form a subcommittee of 3 members. How many ways can they choose the subcommittee members?
8. In a race with 4 participants, how many ways can the gold, silver, and bronze medals be awarded?
9. How many ways can 3 different prizes be distributed among 5 participants if each participant can receive only one prize?
10. A snack pack is made by choosing 1 drink from 3 options and 2 different snacks from 5 options. The two snacks are chosen as a pair (order does not matter), but the drink choice is separate. What is the number of possible snack packs?
11. A team has 6 players and needs to choose 2 captains (Captain 1 and Captain 2). Since the roles are distinct, order matters. In how many ways can the captains be chosen?
12. A student has 6 different books and wants to place exactly 4 of them on a shelf in a row. Since the left-to-right order on the shelf matters, how many possible arrangements of 4 books chosen from the 6 are there?
13. How many permutations of 6 distinct items taken 3 at a time are there? (That is, how many ordered arrangements of length 3 can be formed from 6 different items?)
14. A student must choose 1 drink and 1 snack. There are 4 drink options and 5 snack options. If any drink can be paired with any snack, what is the number of possible pairs?
15. How many ways can you arrange 3 red balls and 2 blue balls in a row?
16. A password consists of 3 different letters chosen from the alphabet (26 letters). How many such passwords can be made?
17. A club has 8 members. The club needs to choose 3 members to serve on a committee, and the roles are identical (so order does not matter). How many different committees are possible?
18. In how many ways can 2 chefs be chosen from 5 available chefs to prepare a meal?
19. What is the number of arrangements of 5 different colored beads on a string?
20. A student has 6 different books (A, B, C, D, E, F) and wants to arrange exactly 4 of them on a shelf in a row. Since the order on the shelf matters, how many possible arrangements are there?
21. A team has 9 players. The coach wants to select 4 players to travel, and the order does not matter. How many different groups of 4 players can be selected?
22. A pizza shop offers 6 toppings. A customer chooses exactly 2 different toppings. Since the order of toppings does not matter, how many different 2-topping pizzas are possible?
23. In how many different ways can a committee of 4 be selected from a group of 7 people?
24. A debate team consists of 8 students. The coach must select exactly 3 students to form a panel for an upcoming competition. How many different 3-student panels can be formed?
25. A committee of 3 students is to be chosen from a group of 5 seniors and 4 juniors. How many different committees can be formed that consist of exactly 2 seniors and 1 junior?
26. In how many ways can you choose 3 fruits from a basket of 6 different fruits?
27. How many permutations of 5 letters taken 3 at a time?
28. A deck of 52 cards is shuffled. How many ways can the top 5 cards be drawn?
29. A student has 6 different photos and wants to arrange exactly 3 of them in a row in a frame. Since the order in the frame matters, how many possible arrangements are there?
30. A teacher has 7 different students and wants to choose a president and a vice president. Since the two roles are different, order matters. In how many ways can the two officers be selected?
31. In how many ways can 4 friends stand in a line for a photograph?
32. How many ways can you choose 2 pencils from 5 of different colors?
33. How many ways can you arrange 4 people in a car with 4 distinct seats?
34. A club has 8 members and needs to choose 3 people to serve on a committee. Since the committee has no positions, order does not matter. How many ways can the 3 people be chosen?
35. How many permutations of 6 distinct items taken 2 at a time are there? (That is, how many ordered pairs can be formed from 6 different items without repetition?)
36. A team has 9 players. The coach will select a starting group of 4 players, with no positions specified. Since order does not matter, how many different groups of 4 can be selected?
37. A code consists of 3 different letters chosen from 6 distinct letters (A–F), and the letters are arranged in order. No letter may repeat. What is the number of possible codes?
38. A teacher has 7 different problems and will assign 3 of them as a quiz in a specific order (Problem 1, then 2, then 3). Since order matters, how many different quizzes are possible?
39. A class has 10 students. The teacher wants to choose 1 student as class president and 1 different student as vice president. Since the positions are different, order matters. In how many ways can the teacher choose the two students?
40. A student has 6 different songs and wants to create a playlist of 3 songs with no repeats. Since the order of songs in the playlist matters, how many playlists are possible?
41. A code is made by arranging 4 different digits chosen from 0 through 9, with no repetition. Since the order of digits matters, how many such codes are possible?
42. A student must choose 2 electives from a list of 6 different electives. The order of the choices does not matter. How many different pairs of electives are possible?
43. A student has 6 different photos and wants to choose 4 of them to put in an album, where the order of the photos in the album does not matter. How many different sets of 4 photos are possible?
44. A student has 7 different pens and wants to place exactly 5 of them into a pencil case in a specific left-to-right order. How many different ordered selections are possible?
45. A student has 6 different books and wants to arrange 4 of them on a shelf in a row. Since the left-to-right order matters, how many different arrangements are possible?
46. A password consists of 3 letters followed by 2 digits. Letters can be any of the 26 English letters and digits can be any of 0–9. Repetition is allowed. What is the number of possible passwords?
47. A student has 5 different stickers and wants to place all 5 in a row on a notebook. Since the order left-to-right matters, how many different arrangements are possible?
48. From 7 different students, a teacher assigns 1 student to be the speaker, 1 to be the writer, and 1 to be the timekeeper. Since the roles are different, order matters. In how many ways can the teacher assign the roles?
49. A restaurant offers 4 appetizers, 3 main dishes, and 2 desserts. A meal consists of choosing exactly one from each category. What is the number of possible meals?
50. A teacher has 6 different stickers and will hand out all 6 to students, one after another, in a specific sequence. Because the sequence of stickers given out matters, how many different sequences are possible?
51. A student has 5 different stickers and wants to place all 5 in a row on a notebook. Since the order matters, how many possible arrangements of the 5 stickers are there?
52. In a race with 9 runners, medals are awarded for 1st, 2nd, and 3rd place. Since finishing positions are distinct, order matters. How many possible medal outcomes are there?
53. A student must answer exactly 2 questions from a set of 6 questions on a quiz. Since only which questions are chosen matters, order does not matter. How many ways can the student choose the questions?
54. A club has 8 members and needs to choose 3 of them to serve on a committee. Since the committee has no positions, order does not matter. How many ways can the committee be chosen?
55. In how many ways can 3 students be selected from a class of 8 to organize an event?
56. A restaurant offers 3 appetizers, 4 main courses, and 2 desserts. How many different meals can be ordered, consisting of one appetizer, one main course, and one dessert?
57. How many ways can 2 students be chosen from a class of 10 students to present a project?
58. How many ways can 2 people be chosen from a group of 8 to serve as a captain and co-captain?
59. How many different ways can the letters of the word 'BANANA' be arranged?
60. A password is created by choosing 3 different digits from 0-9. How many different passwords can be formed?
61. In a game, there are 4 red cards and 6 blue cards. How many ways can 2 red and 2 blue cards be selected?
62. A group of 7 people is planning a hiking trip. If 3 people must stay behind to prepare dinner, how many ways can the hiking group be chosen?
63. In a bag of 6 red marbles and 4 blue marbles, how many ways can you draw 2 red and 1 blue marble?
64. How many different ways can 5 books be arranged on a shelf?
65. A pizza shop offers 6 different toppings. A customer chooses exactly 2 different toppings, and the order of toppings does not matter. How many ways can the customer choose the toppings?
66. A coach has 8 players and needs to choose a lineup of 5 players in a specific batting order (1 through 5). Since the batting order matters, how many possible lineups are there?
67. A box contains 9 different colored marbles. You select exactly 3 marbles to keep, and the order of selection does not matter. How many ways can you choose 3 marbles from 9?
68. A restaurant offers 5 different sandwiches, 3 different sides, and 2 different drinks. A customer chooses exactly one sandwich, one side, and one drink. What is the number of outcomes for this meal choice?
69. A club has 8 students, and it needs to choose 3 of them to be representatives. Because the roles are identical (no president/vice president), order does not matter. How many ways to choose 3 students from 8 are there?
70. A school has 10 students and needs to choose 4 of them to attend a workshop. Since only the set of students matters, order does not matter. How many ways can 4 students be chosen from 10?
71. A lock code consists of 3 digits chosen from {0,1,2,3,4} with no repetition allowed. Since the order of digits matters in a code, what is the number of possible codes?
72. A password consists of 1 letter followed by 2 digits. The letter can be chosen from 5 options (A–E), and each digit can be chosen from 0–9. Digits may repeat. What is the number of possible passwords?
73. What is the number of ways to choose 2 out of 5 distinct marbles?
74. A student rolls a standard 6-sided die and then flips a coin. What is the number of possible outcomes for the ordered pair (die result, coin result)?
75. A debate team consists of 8 students. The coach must select exactly 3 students to form a panel for an upcoming competition. How many different 3-student panels can be formed?