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) = ?

1/12

22/36

None of these

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

1/16

1/8

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

103/108

None of these

10/216

93/108

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

n! Ways

(n – 1)! Ways

(2n)! ways

(n + 1)! Ways

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

256 ways

12 ways

24 ways

4 ways

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

None of these

1/8

3/8

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

144

360

720

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

∞

-1

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

6 ways

2 ways

24 ways

720 ways

10. The sample space for tossing a coin once is

{H, H}

{H}

{H, T}

{T}

11. 19!/19!(19–19)! = ?

Undefined

None of these

12. If ⁿC₁₂ = ⁿC₆ the value of n is

13. The value of ⁵C₂ is

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

P(A) + P(B) – P(A∩B)

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

P(A) + P(B) – P(AUB)

P(A) + P(B)

15.

16. ⁿPᵣ =

n!/(n–r)!

n!/(n–r)!r!

n!/(n+r)!

(n–r)!/n!

17. ⁶P₃ =

120

360

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

720

1440

360

5040

19. 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

1/13

7/52

2/13

None of these

20. 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

21. 8.7.6/3.2.1 =

3!5!/8!

10!

8!/3!5!

10/2!8!

22. If n is any positive integer, then

n! – n(n + 1)!

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

(n + 1)! = (n + 1)(n – 1)!

n! – n (n – 2)!

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

5!/2!

2!/5!

5!.2!

All of these

24. 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

410

260

356

25. ⁴C₄ = ?

250

None of these

124

Page 2 of 3

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

720 ways

6 ways

2 ways

24 ways

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

28. 5 unbiased coins are tossed simultaneously. The probability of getting at least one head is

31/32

1/16

1/32

None of these

29. ⁿPᵣ = ?

n!/(n-r)!

n!/(n+r)!

n/(n-r)

n!/(n+1)!

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

31. 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

None of these

3/8

1/8

2/8

32. 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

11/4165

22/4165

None of these

44/4165

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

None of these

18/216

1/18

1/216

34. 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:

IAANG

INAGA

NAAIG

NAAGI

35. 6.5.4 =

6!/3!

3!/6!

1/6!

36. 5 persons can be seated at a round table in

25 ways

24 ways

None of these

20 ways

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

11/18

7/18

1/18

13/18

38. 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

5/17

3/17

7/17

9/17

39. 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)}

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

1/7

1/10

1/5

1/3

41.

42. 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

645

735

564

43. Factorial of -2 =

None of these

-362880

40320

362880

44. 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

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

A.P

Permutation

Combination

Sequence

46. 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!ϒ!

p!q!r!/n!

p!/q!ϒ!

n!/q!q!ϒ!

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

7/2

7!/2!

7/2

2!/7!

48. 6!/8! =

1/65

1/56

49. 4! + 5! = ?

50. 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

Page 3 of 3

51. ⁴C₄ has the value equal to

None of these

52. ⁶P₄ is equal to

360

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

120

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

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

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

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

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

55. Probability theory was introduced by ___________

German mathematician

American mathematician

French mathematician

British mathematician

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

24 ways

6 ways

720 ways

2 ways

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

Sequence

Identity function

Series

Onto function

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

6!/2!.2!

6!/2²!

6!.2.2!

2²!/6!

59. 1/20.19.18.17 =

20!

16!/20!

1/16!

20!/16!

60. 6P1 is equal to

61. (n+1)n(n–1)/3.2.1 =

(n + 1)!

3!(n–2)/(n+1)

(n+1)/3!(n–2)

(n–2)!

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

None of these

1/3

63. 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

1/18

None of these

1/36

1/12

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

1/26

1/13

2/13

3/13

65. n(n–1)/3.2.1 =

3!(n–2)!/n!

(n – 2)!/3!n!

n!/3!(n–2)!

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

1/3

1/5

1/6

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

(n+2)!/(n–1)

(n + 2)!

(n – 1)!/(n+2)

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

4/9

5/12

7/36

5/9

69. 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

5/12

7/12

1/12

1/6

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

2/3

None of these

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

11!/2³!

2!2!2!/11!.

11!/2!2!2!.

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

72. 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

2/5

4/5

3/5

None of these

73. The value of n, when ⁿP₂ = 20 is

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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