Fundamental principle of counting - Question Bank

1. How many distinct permutations are there of the letters in the word 'BOOK'?
A) 24
B) 12
C) 6
D) 4
2. 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?
A) 7
B) 12
C) 4
D) 3
3. How many ways can a student select one course from a list of 10 elective courses?
A) 1
B) 10
C) 0
D) 100
4. If there are 5 choices for a shirt, 4 choices for pants, and 3 choices for shoes, how many different outfits can be created?
A) 12
B) 60
C) 20
D) 15
5. How many odd numbers can be formed using the digits 1, 2, 3, 4, 5, 6 without repetition, considering only 3-digit numbers?
A) 100
B) 60
C) 80
D) 120
6. 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?
A) 5
B) 6
C) 3
D) 2
7. 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?
A) 15
B) 60
C) 125
D) 20
8. 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?
A) 12
B) 35
C) 5
D) 7
9. A painter has 6 colors. How many ways can she choose 3 different colors to paint a picture, where the order of colors matters?
A) 20
B) 120
C) 18
D) 6
10. How many different paths are there from city A to city B if there are 4 roads connecting them?
A) 1
B) 4
C) 16
D) 8
11. In how many ways can a committee of 3 people be selected from a group of 7 people?
A) 21
B) 35
C) 7
D) 3
12. A coin is tossed 3 times. How many possible sequences of outcomes are there?
A) 6
B) 8
C) 9
D) 3
13. How many ways can a person choose a shirt from 5 options and a pair of pants from 4 options?
A) 9
B) 20
C) 5
D) 4
14. 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?
A) 5
B) 6
C) 3
D) 2
15. How many ways can you travel from point A to point B if there are 3 different bus routes and 2 different train routes?
A) 5
B) 6
C) 3
D) 2
16. 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?
A) 18
B) 80
C) 10
D) 8
17. How many ways can a person choose a password of length 4 using digits 0-9 if repetition is allowed?
A) 10000
B) 256
C) 10
D) 40
18. 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?
A) 22
B) 350
C) 50
D) 70
19. 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?
A) 5
B) 15
C) 31
D) 32
20. A company has 8 employees. In how many ways can a team of 3 employees be selected for a project?
A) 24
B) 56
C) 336
D) 8
21. How many possible outcomes are there when rolling two distinct six-sided dice?
A) 12
B) 36
C) 6
D) 1
22. A person has 4 pairs of shoes and 6 pairs of socks. How many different combinations of shoes and socks can be worn?
A) 10
B) 24
C) 4
D) 6
23. How many ways are there to arrange the letters of the word 'GO'?
A) 1
B) 2
C) 3
D) 4
24. Consider a scenario where you need to choose an outfit from 5 shirts and 3 pants. How many different outfits can you create?
A) 8
B) 15
C) 5
D) 3
25. A bakery offers 7 types of cookies. How many ways can a customer choose 2 different types of cookies?
A) 14
B) 49
C) 42
D) 21
26. 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?
A) 1000
B) 720
C) 30
D) 120
27. 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?
A) 6
B) 9
C) 27
D) 8
28. In how many ways can a student answer a multiple-choice question with 4 options, where only one option is correct?
A) 1
B) 4
C) 3
D) 0
29. A lock has a 3-digit combination using digits 0-9. How many possible combinations are there if repetition of digits is not allowed?
A) 1000
B) 720
C) 270
D) 90
30. 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?
A) 13
B) 40
C) 8
D) 5
31. 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?
A) 125
B) 60
C) 15
D) 10
32. A survey asks individuals to choose one option from 'Yes', 'No', or 'Maybe'. How many possible responses are there for each individual?
A) 1
B) 2
C) 3
D) 0
33. How many possible outcomes are there when drawing one card from a standard deck of 52 playing cards?
A) 4
B) 13
C) 52
D) 26
34. 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?
A) 7
B) 12
C) 3
D) 4
35. How many ways can the letters of the word 'CAT' be arranged?
A) 3
B) 6
C) 9
D) 1
36. 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?
A) 7
B) 12
C) 10
D) 6
37. 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?
A) 100
B) 90
C) 20
D) 10
38. How many possible outcomes are there when flipping a coin and rolling a standard six-sided die simultaneously?
A) 8
B) 6
C) 12
D) 2
39. A painter has 5 different colors of paint. How many ways can she choose 2 different colors to mix?
A) 10
B) 25
C) 5
D) 2
40. 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?
A) 13
B) 42
C) 1
D) 6
41. How many three-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 if repetition of digits is allowed?
A) 60
B) 125
C) 15
D) 75
42. 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?
A) 26
B) 105
C) 16
D) 21
43. 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?
A) 8
B) 15
C) 2
D) 5
44. How many ways are there to select one fruit from a basket containing 5 apples and 4 oranges?
A) 9
B) 20
C) 5
D) 4
45. 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?
A) 5
B) 6
C) 3
D) 2
46. 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?
A) 10
B) 25
C) 20
D) 15
47. 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?
A) 12
B) 15
C) 9
D) 7
48. 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?
A) 10
B) 24
C) 20
D) 12
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?
A) m + n
B) m - n
C) m * n
D) m / n
50. What is the fundamental principle of counting also known as?
A) The Pigeonhole Principle
B) The Principle of Mathematical Induction
C) The Multiplication Principle
D) The Addition Principle
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