MCQ Mathematics Chapter 6: PERMUTATIONS AND COMBINATIONS, HS 1st year

 

1. Mohan has 3 pants and 2 shirts. How many different pairs of a pant and a shirt can he wear?

   • a) 4
   • b) 5
   • c) 6
   • d) 3
     Answer: c) 6

2. Sabnam has 2 school bags, 3 tiffin boxes, and 2 water bottles. In how many ways can she carry one of each item?

   • a) 12
   • b) 10
   • c) 18
   • d) 24
     Answer: a) 12

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MCQs on Permutations

3. How many 4-letter words, with or without meaning, can be formed from the word "ROSE" without repeating letters?

   • a) 12
   • b) 24
   • c) 36
   • d) 48
     Answer: b) 24

4. How many different signals can be generated using 4 flags of different colors, if each signal requires the use of 2 flags, one below the other?

   • a) 10
   • b) 12
   • c) 15
   • d) 20
     Answer: b) 12

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MCQs on Combinations

5. How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 if repetition is not allowed?

   • a) 20
   • b) 30
   • c) 60
   • d) 120
     Answer: c) 60

6. In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?

   • a) 30
   • b) 40
   • c) 60
   • d) 120
     Answer: c) 60

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MCQs on Factorials

7. What is the value of $7!$?

   • a) 5040
   • b) 720
   • c) 40320
   • d) 362880
     Answer: a) 5040

8. Simplify $\frac{7!}{5!}$:

   • a) 6
   • b) 12
   • c) 42
   • d) 120
     Answer: c) 42

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MCQs on Special Arrangements

9. How many 8-letter arrangements can be made from the letters of the word "DAUGHTER" if all vowels occur together?

   • a) 720
   • b) 1440
   • c) 4320
   • d) 2160
     Answer: c) 4320

10. In how many ways can 4 red, 3 yellow, and 2 green discs be arranged in a row if discs of the same color are indistinguishable?

• a) 2520
• b) 1260
• c) 840
• d) 360
  Answer: b) 1260

11. How many 2-digit even numbers can be formed using the digits 1, 2, 3, 4, 5, if repetition is allowed?

    • a) 8
    • b) 10
    • c) 12
    • d) 15
      Answer: b) 10

12. A signal is made using 3 flags, each of a different color, arranged vertically. If there are 5 different colored flags, how many unique signals can be formed?

    • a) 60
    • b) 120
    • c) 20
    • d) 80
      Answer: a) 60

13. In how many ways can a Chairman and a Vice-Chairman be chosen from a group of 12 people, assuming one person cannot hold both positions?

    • a) 66
    • b) 72
    • c) 132
    • d) 144
      Answer: c) 132

14. How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5 if repetition is allowed?

    • a) 125
    • b) 60
    • c) 120
    • d) 150
      Answer: a) 125

15. How many outcomes are possible when a coin is tossed 3 times?

    • a) 6
    • b) 8
    • c) 4
    • d) 16
      Answer: b) 8

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MCQs on Permutations

16. Evaluate $^5P_3$:

    • a) 20
    • b) 30
    • c) 60
    • d) 120
      Answer: c) 60

17. How many permutations are possible for the word “ROOT”?

    • a) 12
    • b) 24
    • c) 6
    • d) 18
      Answer: a) 12

18. In how many ways can the letters of the word “NUMBER” be arranged if repetition is not allowed?

    • a) 720
    • b) 120
    • c) 360
    • d) 480
      Answer: b) 120

19. How many numbers lying between 100 and 1000 can be formed with the digits 0, 1, 2, 3, 4, 5, if repetition is not allowed?

    • a) 120
    • b) 100
    • c) 60
    • d) 80
      Answer: b) 100

20. How many signals can be generated using 5 flags of different colors if each signal requires at least 2 flags?

    • a) 60
    • b) 320
    • c) 120
    • d) 240
      Answer: b) 320

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MCQs on Factorials

21. What is the value of $8!$?

    • a) 40320
    • b) 5040
    • c) 362880
    • d) 720
      Answer: a) 40320

22. Simplify $\frac{12!}{10! \cdot 2!}$:

    • a) 60
    • b) 66
    • c) 120
    • d) 72
      Answer: b) 66

23. Find $n$ such that $^nP_4 = 3024$:

    • a) 9
    • b) 8
    • c) 7
    • d) 10
      Answer: a) 9

24. Calculate $^8C_4$:

    • a) 70
    • b) 56
    • c) 64
    • d) 48
      Answer: a) 70

25. How many permutations can be made by arranging the letters of the word "ALLAHABAD"?

    • a) 2520
    • b) 7560
    • c) 8400
    • d) 5040
      Answer: b) 7560

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MCQs on Combinations

26. How many chords can be drawn through 21 points on a circle?

    • a) 210
    • b) 420
    • c) 231
    • d) 252
      Answer: c) 231

27. How many ways are there to select 3 boys and 2 girls from 5 boys and 4 girls?

    • a) 60
    • b) 40
    • c) 45
    • d) 50
      Answer: a) 60

28. A student must select 5 courses out of 9 available courses, including 2 compulsory ones. In how many ways can they do this?

    • a) 21
    • b) 42
    • c) 35
    • d) 56
      Answer: b) 42

29. How many ways can 2 black balls and 3 red balls be chosen from 5 black and 6 red balls?

    • a) 120
    • b) 200
    • c) 150
    • d) 300
      Answer: a) 150

30. In how many ways can 4 cards be chosen from a deck of 52 cards such that all are of the same suit?

    • a) 2860
    • b) 3640
    • c) 2600
    • d) 2400
      Answer: a) 2860

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MCQs on Arrangements

31. How many distinct permutations can be made from the letters of "EQUATION"?

    • a) 40320
    • b) 20160
    • c) 30240
    • d) 5040
      Answer: c) 30240

32. How many words can be formed using all the letters of "ASSASSINATION" such that all the S's are together?

    • a) 240240
    • b) 60480
    • c) 120120
    • d) 30240
      Answer: b) 60480

33. In how many ways can the letters of "MISSISSIPPI" be arranged so that the four I's do not come together?

    • a) 34560
    • b) 30240
    • c) 28000
    • d) 32000
      Answer: a) 34560

34. How many ways can 5 men and 4 women be seated in a row such that women occupy even places?

    • a) 1440
    • b) 2880
    • c) 5760
    • d) 7200
      Answer: c) 5760

35. How many ways can a cricket team of 11 be selected from 17 players such that it includes exactly 4 bowlers?

• a) 4410
• b) 3570
• c) 5390
• d) 5040
  Answer: d) 5040

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MCQs on Fundamental Counting Principle

36. A bag contains 5 black balls and 6 red balls. How many ways can 3 black and 2 red balls be selected?

    • a) 100
    • b) 120
    • c) 200
    • d) 150
      Answer: d) 150

37. In how many ways can 5 girls and 3 boys be seated in a row such that no two boys sit together?

    • a) 14400
    • b) 12000
    • c) 13000
    • d) 10000
      Answer: a) 14400

38. If a signal consists of 3 flags arranged vertically, how many signals can be formed with 4 different flags?

    • a) 24
    • b) 60
    • c) 12
    • d) 20
      Answer: a) 24

39. How many 4-digit telephone numbers can be formed using digits 0–9 if repetition is not allowed and the number starts with 67?

    • a) 336
    • b) 504
    • c) 720
    • d) 1008
      Answer: a) 336

40. How many outcomes are possible if a coin is tossed 4 times?

    • a) 8
    • b) 12
    • c) 16
    • d) 20
      Answer: c) 16

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MCQs on Permutations

41. Calculate $^7P_4$:

    • a) 840
    • b) 1260
    • c) 1680
    • d) 2520
      Answer: c) 1680

42. How many numbers greater than 100,000 can be formed using all digits of 1, 2, 0, 2, 4, 2, 4?

    • a) 420
    • b) 360
    • c) 300
    • d) 480
      Answer: b) 360

43. How many permutations of the word “INSTITUTE” can be made if all vowels must occur together?

    • a) 4320
    • b) 12600
    • c) 16800
    • d) 20160
      Answer: c) 16800

44. How many ways can 4 red, 2 green, and 3 yellow discs be arranged in a row if discs of the same color are indistinguishable?

    • a) 1260
    • b) 1512
    • c) 840
    • d) 720
      Answer: a) 1260

45. How many words can be formed by arranging all letters of “MONDAY,” assuming no letters are repeated?

    • a) 720
    • b) 5040
    • c) 360
    • d) 120
      Answer: a) 720

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MCQs on Factorials

46. Simplify $\frac{6!}{4! \cdot 2!}$:

    • a) 10
    • b) 15
    • c) 20
    • d) 30
      Answer: b) 15

47. Evaluate $9! - 7!$:

    • a) 362880
    • b) 403200
    • c) 322560
    • d) 725760
      Answer: c) 322560

48. Find $n$ if $^nP_2 = 42$:

    • a) 6
    • b) 7
    • c) 8
    • d) 9
      Answer: b) 7

49. Calculate $8! - 7!$:

    • a) 20160
    • b) 40320
    • c) 241920
    • d) 362880
      Answer: a) 20160

50. What is the value of $^5P_2$?

    • a) 20
    • b) 30
    • c) 10
    • d) 15
      Answer: a) 20

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MCQs on Combinations

51. How many ways can a team of 2 boys and 2 girls be selected from 4 boys and 3 girls?

    • a) 18
    • b) 21
    • c) 24
    • d) 28
      Answer: b) 21

52. How many ways can a cricket team of 11 be formed from 16 players, including 5 bowlers, if the team must include exactly 4 bowlers?

    • a) 4200
    • b) 5040
    • c) 4620
    • d) 4800
      Answer: b) 5040

53. A class has 10 students, including 3 who insist on joining together or none at all. In how many ways can 7 students be selected?

    • a) 105
    • b) 120
    • c) 210
    • d) 252
      Answer: c) 210

54. How many chords can be drawn through 15 points on a circle?

    • a) 105
    • b) 120
    • c) 150
    • d) 210
      Answer: d) 210

55. How many ways can 2 vowels and 3 consonants be selected from the word "DAUGHTER"?

    • a) 50
    • b) 60
    • c) 40
    • d) 30
      Answer: b) 60

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MCQs on Arrangements

56. How many numbers can be formed using the digits 0, 1, 3, 5, 7, and 9 that are divisible by 10 and have no repeated digits?

    • a) 120
    • b) 60
    • c) 24
    • d) 80
      Answer: b) 60

57. How many arrangements can be made from the word “EXAMINATION” so that all vowels appear together?

    • a) 21600
    • b) 30240
    • c) 20160
    • d) 17280
      Answer: c) 20160

58. How many ways can a group of 7 members be formed from 5 boys and 4 girls such that the group includes at least 3 girls?

    • a) 210
    • b) 252
    • c) 196
    • d) 280
      Answer: b) 252

59. How many 6-digit numbers divisible by 5 can be formed using the digits 0, 1, 2, 3, 4, 5, 6, without repetition?

    • a) 120
    • b) 150
    • c) 180
    • d) 200
      Answer: c) 180

60. How many ways can 8 people sit around a circular table?

• a) 40320
• b) 5040
• c) 2520
• d) 720
  Answer: c) 2520

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MCQs on Fundamental Counting Principle

61. If a die is rolled twice, how many total outcomes are possible?

    • a) 12
    • b) 24
    • c) 36
    • d) 42
      Answer: c) 36

62. How many ways can 3 dice show different outcomes when rolled simultaneously?

    • a) 120
    • b) 216
    • c) 90
    • d) 72
      Answer: b) 216

63. In how many ways can a 6-character password be formed using only digits (0-9) if repetition is allowed?

    • a) $10^6$
    • b) $6!$
    • c) $10!$
    • d) $60$
      Answer: a) $10^6$

64. If you have 4 types of ice cream flavors and 3 types of cones, how many combinations of a single flavor with a cone can you create?

    • a) 12
    • b) 9
    • c) 7
    • d) 15
      Answer: a) 12

65. A menu has 3 appetizers, 4 main courses, and 2 desserts. How many complete meals can you order (one from each category)?

    • a) 24
    • b) 36
    • c) 48
    • d) 60
      Answer: b) 24

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MCQs on Permutations

66. Find $^6P_2$:

    • a) 30
    • b) 36
    • c) 42
    • d) 60
      Answer: d) 60

67. How many arrangements can be made from the word “SCHOOL” if no letter is repeated?

    • a) 720
    • b) 600
    • c) 360
    • d) 240
      Answer: a) 720

68. How many ways can the letters of "MIRROR" be arranged if the R's are identical?

    • a) 60
    • b) 120
    • c) 240
    • d) 360
      Answer: a) 60

69. In how many ways can a president and vice president be chosen from a group of 8 people?

    • a) 56
    • b) 64
    • c) 72
    • d) 90
      Answer: c) 72

70. How many unique permutations of the word "BANANA" are possible?

    • a) 60
    • b) 120
    • c) 720
    • d) 360
      Answer: a) 60

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MCQs on Combinations

71. How many ways can you select 4 cards from a deck of 52?

    • a) 270725
    • b) 124850
    • c) 134596
    • d) 298560
      Answer: a) 270725

72. How many combinations of 3 flavors can be selected from 6 available ice cream flavors?

    • a) 20
    • b) 30
    • c) 40
    • d) 15
      Answer: d) 15

73. How many ways can a committee of 4 be chosen from 10 people?

    • a) 120
    • b) 210
    • c) 252
    • d) 360
      Answer: b) 210

74. How many ways can 2 boys and 2 girls be selected from 5 boys and 5 girls?

    • a) 100
    • b) 120
    • c) 150
    • d) 200
      Answer: b) 120

75. How many ways can a cricket team of 11 players be selected from a pool of 20?

    • a) 184756
    • b) 203580
    • c) 215441
    • d) 230000
      Answer: a) 184756

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MCQs on Factorials

76. Simplify $\frac{8!}{6! \cdot 2!}$:

    • a) 28
    • b) 32
    • c) 24
    • d) 40
      Answer: c) 28

77. Calculate $(7!)^2$:

    • a) 40320
    • b) 1625702400
    • c) 101606400
    • d) 725760
      Answer: b) 1625702400

78. Evaluate $9! / (5! \times 4!)$:

    • a) 9
    • b) 12
    • c) 21
    • d) 15
      Answer: c) 21

79. Find $n$ such that $^nC_3 = 84$:

    • a) 9
    • b) 10
    • c) 7
    • d) 8
      Answer: b) 10

80. Find the value of $n$ if $^nP_2 = 110$:

    • a) 10
    • b) 11
    • c) 12
    • d) 9
      Answer: b) 11

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MCQs on Arrangements

81. How many distinct arrangements can be made from the letters of "EXPRESSION" such that all vowels appear together?

    • a) 21600
    • b) 30240
    • c) 17280
    • d) 12000
      Answer: c) 17280

82. How many arrangements can be made from the letters of “CALCULATE” if all L's must occur together?

    • a) 30240
    • b) 15120
    • c) 20160
    • d) 10080
      Answer: b) 15120

83. How many distinct arrangements can be made from "STATISTICS" where the S's do not occur together?

    • a) 100800
    • b) 120960
    • c) 60480
    • d) 30240
      Answer: a) 100800

84. In how many ways can 3 men and 3 women be arranged in a row such that no two men sit next to each other?

    • a) 720
    • b) 1440
    • c) 2400
    • d) 3600
      Answer: b) 1440

85. How many numbers can be formed using the digits 1, 2, 3, 4, 5, 6, and 7 that are divisible by 5?

    • a) 720
    • b) 600
    • c) 504
    • d) 840
      Answer: c) 504

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MCQs on Advanced Applications

86. How many ways can you arrange 7 people in a circular table?

    • a) 720
    • b) 5040
    • c) 1440
    • d) 120
      Answer: d) 120

87. How many ways can a football team of 11 players be arranged from a pool of 22 players if there must be 5 defenders?

    • a) 50050
    • b) 90000
    • c) 60000
    • d) 50400
      Answer: a) 50050

88. In how many ways can 4 vowels and 3 consonants be arranged in the word "ADVANTAGE"?

    • a) 15120
    • b) 20160
    • c) 10080
    • d) 7200
      Answer: b) 20160

89. How many ways can a school select a group of 3 teachers and 2 students from a total of 6 teachers and 8 students?

    • a) 560
    • b) 720
    • c) 840
    • d) 960
      Answer: c) 840

90. How many passwords of length 5 can be made using only letters (A-Z), if no letter is repeated?

• a) 7893600
• b) 3802040
• c) 6587800
• d) 1411200
  Answer: d) 1411200

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