Mathematics Permutations Combinations and Probability Online Test

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Maan AliLast Updated: October 15, 2025

Start your preparation for Mathematics Permutations Combinations and Probability Online Test. This online test contains important MCQs from past papers. Attempting this test will help you prepare for Annual Exams and Entry Tests. Read the questions carefully and select the correct option below to see your result.

Important Math Permutations Combinations and Probability Question and Answer

Total Questions:	74
Time Allowed:	40 Minutes
Total Marks:	74
How to Attempt Test:	Please choose the right Option in MCQ-type question.
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Math Permutations Combinations and Probability Practice Test Online With Explanation

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Page 1 of 3

Math

1. If n (E₁) = 18 and n (E₂) = 6 and n (5) = 36 also E₁ and E₂ are independent then P(E₁ ∩ E₂) = ?

None of these

22/36

1/12

2. In how many ways can the letters of the word ‘LEADER’ be arranged?

720

360

144

3. A card is drawn from a pack of cards numbered 1 to 52, the probability that the number on the card is a perfect square is

7/52

None of these

1/13

2/13

4. 1/20.19.18.17 =

20!/16!

20!

1/16!

16!/20!

5. If n is any positive integer, then

(n + 1)! = (n + 1)(n – 1)!

n! – n (n – 2)!

(n+1)! = (n + 1) n!

n! – n(n + 1)!

6. Probability theory was introduced by ___________

German mathematician

British mathematician

American mathematician

French mathematician

7. Six boys and 3 girls are to be seated at random, in a row, for a photograph. The probability that no two girls will sit together is

1/6

5/12

1/12

7/12

8. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how ways can it be done?

756

564

645

735

9. ⁿPᵣ = ?

n!/(n+r)!

n/(n-r)

n!/(n-r)!

n!/(n+1)!

10. A die is rolled, what is the probability of getting a number which is even and greater than 2?

1/6

1/3

None of these

11. Two dice are thrown simultaneously find the probability that the sum of the dots of the dice is a prime no?

5/9

4/9

7/36

5/12

12. The letters of the CHORD taken all at a time can be written in

720 ways

2 ways

24 ways

6 ways

13.

14. ⁶P₃ =

360

120

15. The probability that a 3 – digit no. chosen at random divisible by 5 is

1/3

1/7

1/5

1/10

16. From a group of 5 men and 3 women, a committee of 4 persons is to be selected randomly. The probability that there is a majority of men is

1/6

1/3

17. 5 persons can be seated at a round table in

25 ways

None of these

20 ways

24 ways

18. Three dice are thrown together. The probability of getting a total of at least 6 is

None of these

93/108

10/216

103/108

19. n(n–1)/3.2.1 =

3!(n–2)!/n!

(n – 2)!/3!n!

n!/3!(n–2)!

20. How many signals can be given with three different flags when any number of them may be used

21. (n + 2)(n + 1) n =

(n + 2)!

(n – 1)!/(n+2)

(n+2)!/(n–1)

22. The number of permutations of the n objects of which there are p like objects of one kind, q like objects of the second kind nd r like objects of the third kind are

n!/q!q!ϒ!

n!/q!ϒ!

p!q!r!/n!

p!/q!ϒ!

23. If A is an impossible event then P(A) = ?

∞

-1

24. In different objects can be arranged taken all at a time in

(2n)! ways

(n + 1)! Ways

n! Ways

(n – 1)! Ways

25. In a class of 100 students, 60 drink tea, 50 drink coffee and 30 drink both. A student from this class is selected at random. The probability that the student takes at last one of 2 drinks is

None of these

2/5

4/5

3/5

Page 2 of 3

26. 6!/8! =

1/65

1/56

27. If ⁿC₁₂ = ⁿC₆ the value of n is

28.

29. 6.5.4 =

6!/3!

3!/6!

1/6!

30. Events A, B and C are equally likely when

P(A) + P(B) = P(C)

P(A) = P(B) = P(C)

P(A) = P(B) + P(C)

P(B) = P(A) + (PC)

31. ⁿPᵣ =

n!/(n+r)!

n!/(n–r)!r!

(n–r)!/n!

n!/(n–r)!

32. An unbiased die is thrown. Then the probability of getting a prime is

2/3

None of these

33. The number of words that can be formed out of the letters of the word BANNU is

5!/2!

5!.2!

2!/5!

All of these

34. Two cards are drawn at random from a well shuffled pack of cards. The probability that at least one of them is a face card is

9/17

7/17

3/17

5/17

35. The number of significant numbers which can be formed by using any number of the digits 0, 1, 2, 3, 4 but using each not more than once in each number is

356

260

410

36. If A and Bare mutually exclusive then P(AUB) = ?

P(A) + P(B)+P(AUB)

P(A) + P(B)

P(A) + P(B) – P(A∩B)

P(A) + P(B) – P(AUB)

37. The number of words that can be formed out of the letters of the word PHYSICS is

7!/2!

7/2

2!/7!

38. What is the probability to get a block jack from a well shuffled pack of playing cards?

3/13

1/13

1/26

2/13

39. If 4 ⁶Pᵣ = ⁶Pᵣ₊₁, then r is equal to

40. A number is selected at random form the three digit numbers, the probability that the number is divisible by 4 is

1/8

1/16

41. The number of words that can be formed out of the letters of the word MURREE is

2²!/6!

6!/2²!

6!.2.2!

6!/2!.2!

42. The sample space for tossing a coin once is

{H, T}

{H, H}

{H}

{T}

43. 19!/19!(19–19)! = ?

Undefined

None of these

44. The value of n, when ⁿP₂ = 20 is

45. Two unbiased dice are thrown. The probability that the total score is > 5 is

11/18

1/18

7/18

13/18

46. ⁴C₄ = ?

250

124

None of these

47. In how many ways can 7 keys be arranged in a circular key ring

1440

360

720

5040

48. The letters of the JUNE taken all a t a time can be written in

24 ways

6 ways

720 ways

2 ways

49. A bad contains 3 white, 4 black and 2 red balls. If 2 balls are drawn at random, then the probability that both the balls are white is

1/12

None of these

1/36

1/18

50. Two balanced dice are tossed once, the sample space when the integers on the faces of two dice are the same is

None of these

{(1, 1),(2, 2),(3, 3)}

{(1, 1),(2, 2),(3, 3),(4, 4),(5, 5),(6, 6)}

{(4, 4),(5, 5),(6, 6)}

Page 3 of 3

51. Three unbiased coins are tossed. Then the probabilities of getting two heads is

1/8

3/8

None of these

52. (n+1)n(n–1)/3.2.1 =

(n–2)!

3!(n–2)/(n+1)

(n+1)/3!(n–2)

(n + 1)!

53. ⁴C₄ has the value equal to

None of these

54. All letters of the word “AGAIN” are permuted in all possible ways and the words so formed (with or without meaning) are written as in dictionary, then the 50th word is:

NAAGI

NAAIG

INAGA

IAANG

55. 4! + 5! = ?

56. Factorial of -2 =

-362880

None of these

40320

362880

57. 5 unbiased coins are tossed simultaneously. The probability of getting at least one head is

1/32

None of these

31/32

1/16

58. 6P1 is equal to

59. An arrangement of a finite number of objects taken some or all at a time is called their

Permutation

Sequence

A.P

Combination

60. Four cards are drown at random from a pack of 52 playing cards. The probability of getting all the four cards of the same suit is

22/4165

44/4165

11/4165

None of these

61. Riaz, Saba, Maria, Shehzad are to give speeches in a class. The teacher can arrange the order of their presentation in

24 ways

256 ways

12 ways

4 ways

62. A coin is tossed. If head comes up, a die is thrown but if tail comes up, the coin is tossed again. The probability of obtaining a head and an even number is

2/8

None of these

1/8

3/8

63. If probability of rain today is 1/3 what is probability of not rain today?

1/3

None of these

64. The probability of getting 5, when one dice is called

1/3

1/5

1/6

65. If probability of bulb being defective is 0.2. estimate how many defective bulb there would be in 600 bulbs

120

66. The number of words that can be formed out of the letters of the word MATHEMATICS is

2!2!2!/11!.

11!/2!.2!.2!.

11!/2³!

11!/2!2!2!.

67. The value of ⁵C₂ is

68. 8.7.6/3.2.1 =

10/2!8!

10!

3!5!/8!

8!/3!5!

69. A function whose domain is the set of natural numbers is called the

Sequence

Onto function

Identity function

Series

70. ⁶P₄ is equal to

360

71. The letters of the LAHORE taken all at a time can be written in

720 ways

6 ways

2 ways

24 ways

72. There dice are thrown simultaneously find the probability to get greatest sum of dost?

None of these

1/216

18/216

1/18

73. There are 25 tickets bearing numbers from 1 to 25. One ticket is drawn at random. The probability that the number on it is a multiple of 5 or 6 is

None of these

7/25

9/25

11/25

M-CAT-Q

74. 0!

-1

How to Score High in Mathematics Permutations Combinations and Probability Online Test?

Mastering scientific subjects requires conceptual clarity.

Key Preparation Tips:

Concepts First: Ensure you understand the underlying theories before attempting the MCQs.
Time Management: Attempt this online quiz multiple times to improve your speed.

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7 Comments

Anaya says:

February 11, 2022 at 2:28 pm

How i prepare msc math entry test

zohaib says:

July 29, 2017 at 12:37 am

i got 100%

Qasim Ali says:

July 15, 2017 at 11:29 pm

whats the right answer for this mcq’s arrangment of fintite number of objects taken some or all the time??? i have confusion with this

Karan Kumar says:

May 4, 2017 at 1:52 pm

I got 96%. Only 1 mistake.

umair ahmed says:

March 19, 2017 at 1:05 pm

92%

Aunali says:

July 31, 2016 at 11:37 am

i got 96%

AMEER HAMZA says:

July 21, 2016 at 9:01 pm

GREAT PEOPLE DOING THIER JOB IN THEV BEST POSSIBLE WAY

Important Math Permutations Combinations and Probability Question and Answer

Math Permutations Combinations and Probability Practice Test Online With Explanation

Math

M-CAT-Q

How to Score High in Mathematics Permutations Combinations and Probability Online Test?

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