Probability, Permutation and Combination - Question Bank

1. What is the probability that a randomly chosen 3-digit number is divisible by 5?
A) 1/5
B) 1/10
C) 1/9
D) 1/3
2. In how many ways can 5 men and 2 women be seated in a row so that the two women are always together?
A) 1440
B) 720
C) 240
D) 360
3. A fair die is rolled twice. What is the probability of getting a sum of 10?
A) 3/36
B) 1/36
C) 2/36
D) 4/36
4. What is the probability of selecting a number divisible by 7 from the integers 1 to 50?
A) 7/50
B) 6/50
C) 8/50
D) 5/50
5. How many ways can the letters of the word 'ENGINEERING' be arranged?
A) 11! / (3! * 3! * 2!)
B) 11! / (3! * 2! * 2!)
C) 11! / (3! * 3! * 2! * 1!)
D) 11! / (3! * 3!)
6. If nC(r-1) : nCr : nC(r+1) = 1:2:3, find n.
A) 7
B) 8
C) 9
D) 10
7. What is the probability that a year chosen at random contains 53 Sundays?
A) 1/7
B) 2/7
C) 1/4
D) 1/365
8. How many ways can 5 different prizes be distributed among 5 students, if each student gets one prize?
A) 5
B) 25
C) 120
D) 10
9. What is the probability of drawing a red ball or a blue ball from a bag containing 5 red, 3 blue, and 2 green balls?
A) 8/10
B) 5/10
C) 3/10
D) 10/10
10. A letter is chosen at random from the word 'ASSASSINATION'. What is the probability that it is an 'S'?
A) 3/13
B) 4/13
C) 1/13
D) 5/13
11. How many ways can a committee of 4 men and 3 women be formed from 7 men and 5 women?
A) 7C4 * 5C3
B) 7P4 * 5P3
C) (7+5)C(4+3)
D) 7C3 * 5C4
12. What is the total number of possible outcomes when rolling two distinct dice?
A) 12
B) 36
C) 6
D) 18
13. If P(A) = 0.6, P(B) = 0.5, and P(A ∪ B) = 0.8, what is P(A ∩ B)?
A) 0.3
B) 0.2
C) 0.1
D) 0.4
14. In how many ways can 6 students be seated in a row if two specific students must sit together?
A) 720
B) 120
C) 144
D) 240
15. What is the probability of picking a prime number from the integers 1 to 10?
A) 4/10
B) 5/10
C) 3/10
D) 6/10
16. How many diagonals does a polygon with 10 sides have?
A) 45
B) 35
C) 50
D) 10
17. What is the probability that a number selected from 1 to 30 is a multiple of 3?
A) 10/30
B) 9/30
C) 3/30
D) 1/3
18. A coin is tossed 5 times. What is the probability of getting at least one head?
A) 1/32
B) 31/32
C) 16/32
D) 1/2
19. How many ways can a president, vice-president, and treasurer be selected from a club of 15 members?
A) 15C3
B) 15P3
C) 15*3
D) 15+3
20. What is the probability of drawing two kings from a deck of 52 cards without replacement?
A) (4/52) * (4/52)
B) (4/52) * (3/51)
C) (4/52) + (3/51)
D) (4/52) * (4/51)
21. If nCr = 10 and n = 5, what is r?
A) 2
B) 3
C) 2 or 3
D) 1
22. What is the probability of selecting a vowel from the letters of the word 'EDUCATION'?
A) 5/9
B) 4/9
C) 1/9
D) 5/4
23. How many ways can 5 distinct books be arranged on a shelf?
A) 5
B) 25
C) 120
D) 60
24. If nPr = 720 and n = 6, what is r?
A) 3
B) 4
C) 5
D) 6
25. What is the probability of getting exactly 2 heads in 4 coin tosses?
A) 4C2 * (1/2)^4
B) 4C1 * (1/2)^4
C) 4C2 * (1/2)^2
D) 2/4
26. What is the total number of ways to arrange 3 men and 3 women in a row such that all men sit together?
A) 720
B) 144
C) 36
D) 6
27. A bag contains 5 green and 7 yellow balls. If two balls are drawn without replacement, what is the probability that both are green?
A) (5/12) * (4/11)
B) (5/12) * (5/11)
C) (5/12) * (7/11)
D) (5/12) + (4/11)
28. How many permutations are possible with the letters of the word 'SUCCESS'?
A) 5040
B) 420
C) 7!/3!2!
D) 7!/3!2!1!
29. What is the probability of drawing a black card or a king from a standard deck of 52 cards?
A) 32/52
B) 26/52
C) 28/52
D) 30/52
30. How many ways can a team of 5 players be selected from 12 players?
A) 12C5
B) 12P5
C) 5! * 12
D) 12/5
31. If P(A) = 0.5, what is the probability of the complement of A, P(A')?
A) 0.5
B) 0
C) 1
D) 0.25
32. What is the probability that a randomly selected year is a leap year?
A) 1/4
B) 1/3
C) 1/5
D) 1/100
33. In how many ways can the first three positions in a race be filled by 10 contestants?
A) 1000
B) 720
C) 240
D) 120
34. How many distinct arrangements are there of the letters in the word 'BANANA'?
A) 720
B) 120
C) 60
D) 360
35. What is the total number of possible outcomes when tossing three fair coins?
A) 3
B) 6
C) 8
D) 9
36. If P(A) = 0.3 and P(B) = 0.4, and A and B are independent events, what is P(A ∩ B)?
A) 0.12
B) 0.7
C) 0.1
D) 0.012
37. From a deck of 52 cards, one card is drawn. What is the probability of drawing an Ace?
A) 1/52
B) 4/52
C) 13/52
D) 1/4
38. How many ways can 4 people be arranged in a line?
A) 16
B) 24
C) 12
D) 4
39. What is the value of 0!?
A) 0
B) 1
C) Undefined
D) Infinity
40. A bag contains 4 red balls and 6 blue balls. If one ball is drawn at random, what is the probability that it is red?
A) 4/10
B) 6/10
C) 4/6
D) 10/4
41. Two dice are rolled simultaneously. What is the probability of getting a sum of 7?
A) 1/36
B) 6/36
C) 5/36
D) 7/36
42. What is the number of combinations of n distinct objects taken r at a time, denoted as nCr?
A) n! / (n-r)!
B) n! / r!
C) (n-r)! / n!
D) n! / (r! * (n-r)!)
43. What is the number of permutations of n distinct objects taken r at a time, denoted as nPr?
A) n! / (n-r)!
B) n! / r!
C) (n-r)! / n!
D) n! / (r! * (n-r)!)
44. In how many ways can a committee of 3 people be chosen from a group of 5 people?
A) 10
B) 15
C) 60
D) 5
45. A fair die is rolled. What is the probability of getting a number greater than 4?
A) 1/6
B) 2/6
C) 3/6
D) 4/6
46. A fair coin is tossed once. What is the probability of getting a head?
A) 1/2
B) 1/3
C) 1
D) 0
47. How many ways can the letters of the word 'APPLE' be arranged?
A) 120
B) 60
C) 240
D) 100
48. What is the value of 5! (5 factorial)?
A) 120
B) 100
C) 60
D) 24
49. If P(A) = 0.6 and P(B) = 0.7, and P(A ∩ B) = 0.4, what is P(A ∪ B)?
A) 0.9
B) 0.7
C) 0.8
D) 1.0
50. What is the probability of an impossible event?
A) 1
B) 0.5
C) 0
D) Undefined
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