Fundamental principle of counting - One Line Questions

1. A survey asks individuals to choose one option from 'Yes', 'No', or 'Maybe'. How many possible responses are there for each individual? — 3
2. In how many ways can a student answer a multiple-choice question with 4 options, where only one option is correct? — 4
3. How many ways are there to arrange the letters of the word 'GO'? — 2
4. How many different paths are there from city A to city B if there are 4 roads connecting them? — 4
5. How many ways can a student select one course from a list of 10 elective courses? — 10
6. A restaurant offers 4 appetizers and 6 main courses. How many different meal combinations are possible if a meal consists of one appetizer and one main course? — 24
7. Consider the task of forming a two-digit number using the digits 1, 2, 3, 4, and 5 without repetition. How many such numbers can be formed? — 20
8. A painter has 5 different colors of paint. How many ways can she choose 2 different colors to mix? — 10
9. A person has 4 pairs of shoes and 6 pairs of socks. How many different combinations of shoes and socks can be worn? — 24
10. An office has 10 employees. In how many ways can a president and a vice-president be selected if one person cannot hold both positions? — 90
11. How many odd numbers can be formed using the digits 1, 2, 3, 4, 5, 6 without repetition, considering only 3-digit numbers? — 60
12. A lock has a 3-digit combination using digits 0-9. How many possible combinations are there if repetition of digits is not allowed? — 720
13. How many ways can a president, vice-president, and treasurer be selected from a club of 10 members, assuming no member can hold more than one position? — 720
14. How many ways can a person choose a password of length 4 using digits 0-9 if repetition is allowed? — 10000
15. In how many ways can a student choose a subject from Physics, Chemistry, and Biology if there are 3, 4, and 5 different courses available in each subject respectively? — 12
16. How many possible outcomes are there when rolling two distinct six-sided dice? — 36
17. How many ways can a student choose one mathematics book and one physics book from a shelf containing 5 mathematics books and 7 physics books? — 35
18. If there are 5 choices for a shirt, 4 choices for pants, and 3 choices for shoes, how many different outfits can be created? — 60
19. Consider the task of painting a house with 3 rooms. If there are 5 different colors available for each room, and each room must be painted a different color, how many ways can the house be painted? — 60
20. Suppose there are 6 roads connecting town X to town Y, and 7 roads connecting town Y to town Z. How many ways can one travel from X to Z through Y? — 42
21. How many ways can a person choose a main course from a menu with 8 options and a dessert from a menu with 5 options? — 40
22. A bakery offers 7 types of cookies. How many ways can a customer choose 2 different types of cookies? — 21
23. Consider the task of forming a 3-letter word using the letters A, B, C, D, E, where repetition is not allowed. How many such words can be formed? — 60
24. A library has 10 fiction books and 8 non-fiction books. How many ways can a reader choose one fiction book and one non-fiction book? — 80
25. A painter has 6 colors. How many ways can she choose 3 different colors to paint a picture, where the order of colors matters? — 120
26. In how many ways can a committee of 3 people be selected from a group of 7 people? — 35
27. Consider a menu with 5 appetizers, 10 main courses, and 7 desserts. How many different meals consisting of one appetizer, one main course, and one dessert can be ordered? — 350
28. A company has 8 employees. In how many ways can a team of 3 employees be selected for a project? — 56
29. How many distinct permutations are there of the letters in the word 'BOOK'? — 12
30. A code word is to be formed by selecting one consonant and one vowel from the English alphabet. If there are 21 consonants and 5 vowels, how many such code words can be formed? — 105
31. How many ways can the letters of the word 'CAT' be arranged? — 6
32. How many possible outcomes are there when drawing one card from a standard deck of 52 playing cards? — 52
33. A person has 3 shirts and 2 pairs of trousers. How many different outfits can be created by wearing one shirt and one pair of trousers? — 6
34. How many different signals can be made by using flags of different colors, choosing at least one flag at a time, if 5 different flags are available? — 31
35. How many ways can you travel from point A to point B if there are 3 different bus routes and 2 different train routes? — 5
36. If a number can be formed by choosing a digit from {1, 2, 3} for the tens place and a digit from {4, 5} for the units place, how many such two-digit numbers can be formed? — 6
37. A person wants to buy a pen. There are 3 brands, and each brand offers 2 ink colors. How many different pen choices does the person have? — 6
38. A factory produces 3 types of products. Each product can be either defective or non-defective. How many possible outcomes are there for a batch of 3 products? — 8
39. A coin is tossed 3 times. How many possible sequences of outcomes are there? — 8
40. How many three-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 if repetition of digits is allowed? — 125
41. A committee of 2 members is to be formed from a group of 4 men and 3 women. How many different committees can be formed if the committee must consist of one man and one woman? — 12
42. A person wants to buy a car. There are 3 models available, and each model comes in 4 different colors. How many different choices does the person have? — 12
43. A restaurant offers 4 types of sandwiches and 3 types of drinks. How many different lunch combinations are possible if a lunch consists of one sandwich and one drink? — 12
44. If there are 5 routes from city A to city B and 3 routes from city B to city C, how many distinct routes are there from city A to city C via city B? — 15
45. How many possible outcomes are there when flipping a coin and rolling a standard six-sided die simultaneously? — 12
46. Consider a scenario where you need to choose an outfit from 5 shirts and 3 pants. How many different outfits can you create? — 15
47. How many ways are there to select one fruit from a basket containing 5 apples and 4 oranges? — 9
48. How many ways can a person choose a shirt from 5 options and a pair of pants from 4 options? — 20
49. If an event can occur in 'm' different ways and another independent event can occur in 'n' different ways, in how many ways can both events occur in succession? — m * n
50. What is the fundamental principle of counting also known as? — The Multiplication Principle
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