Permutation, Combination and Probability MCQs

Permutation, Combination and Probability MCQs

Permutation, Combination and Probability - Multiple Choice Questions

Instructions: This quiz contains 55 multiple-choice questions on permutation, combination and probability. Click the "Show Answers" button to highlight the correct answers in yellow.

01The value of nPr is:
(A) n!/(n-r)!    (B) n!/r!(n-r)!    (C) n!/r!    (D) (n-r)!/n!
02The value of nCr is:
(A) n!/(n-r)!    (B) n!/r!(n-r)!    (C) n!/r!    (D) r!/n!(n-r)!
03If nC8 = nC12, then n = ?
(A) 10    (B) 20    (C) 18    (D) 25
04How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition?
(A) 24    (B) 60    (C) 120    (D) 125
05The probability of getting a head when tossing a fair coin is:
(A) 0    (B) 1/2    (C) 1    (D) 2
06If nPr = 720 and nCr = 120, then r = ?
(A) 2    (B) 3    (C) 4    (D) 5
07In how many ways can 5 people sit in a row?
(A) 25    (B) 120    (C) 60    (D) 240
08The probability of an impossible event is:
(A) 0    (B) 1    (C) 1/2    (D) ∞
09If nC2 = 45, then n = ?
(A) 8    (B) 10    (C) 9    (D) 11
10How many words can be formed from the letters of the word "MATHS"?
(A) 24    (B) 120    (C) 60    (D) 720
11The probability of getting a prime number when a die is thrown is:
(A) 1/2    (B) 1/2    (C) 2/3    (D) 1/3
12Number of diagonals in a hexagon is:
(A) 6    (B) 9    (C) 12    (D) 18
13If P(A) = 0.3 and P(B) = 0.4, and A and B are independent, then P(A∩B) = ?
(A) 0.7    (B) 0.12    (C) 0.12    (D) 0.1
14In how many ways can 4 books be arranged on a shelf?
(A) 16    (B) 24    (C) 12    (D) 8
15The value of 0! is:
(A) 1    (B) 0    (C) ∞    (D) Not defined
16If P(A) = 0.6, then P(A') = ?
(A) 0.4    (B) 0.4    (C) 0.6    (D) 0.3
17How many triangles can be formed from 8 non-collinear points?
(A) 56    (B) 56    (C) 28    (D) 64
18The probability of getting a sum of 7 when two dice are thrown is:
(A) 1/6    (B) 1/6    (C) 1/12    (D) 1/36
19If nP3 = 60, then n = ?
(A) 4    (B) 5    (C) 6    (D) 7
20In how many ways can 5 boys and 3 girls be seated in a row so that no two girls are together?
(A) 14400    (B) 14400    (C) 7200    (D) 28800
21If A and B are mutually exclusive events, then P(A∪B) = ?
(A) P(A)P(B)    (B) P(A) + P(B)    (C) P(A) + P(B) - P(A∩B)    (D) 0
22The number of ways to arrange the letters of the word "BANANA" is:
(A) 720    (B) 60    (C) 120    (D) 360
23If P(A) = 1/3, P(B) = 1/4, and P(A∩B) = 1/12, then A and B are:
(A) Mutually exclusive    (B) Independent    (C) Dependent    (D) Complementary
24How many 4-digit numbers can be formed using digits 0,1,2,3,4,5 without repetition?
(A) 120    (B) 300    (C) 360    (D) 625
25The probability of getting at least one head when two coins are tossed is:
(A) 1/4    (B) 1/2    (C) 3/4    (D) 1
26If nCr = nCr+1, then nCr-1 = ?
(A) nCr    (B) n+1Cr    (C) n-1Cr    (D) nCr+2
27In how many ways can 6 people be seated around a circular table?
(A) 720    (B) 120    (C) 60    (D) 360
28The probability that a leap year has 53 Sundays is:
(A) 1/7    (B) 2/7    (C) 3/7    (D) 4/7
29If 15Cr = 15Cr+3, then r = ?
(A) 3    (B) 6    (C) 9    (D) 12
30How many words can be formed from the letters of the word "COMMITTEE"?
(A) 362880    (B) 45360    (C) 90720    (D) 22680
31If P(A) = 0.4, P(B) = 0.5, and P(A∩B) = 0.2, then P(A|B) = ?
(A) 0.1    (B) 0.4    (C) 0.5    (D) 0.8
32The number of ways to select a cricket team of 11 from 15 players is:
(A) 15!    (B) 1365    (C) 32760    (D) 39916800
33If three coins are tossed, the probability of getting exactly two heads is:
(A) 1/8    (B) 3/8    (C) 1/2    (D) 5/8
34In how many ways can 4 red and 3 blue balls be arranged in a row?
(A) 7!    (B) 35    (C) 840    (D) 5040
35If P(A) = 2/3, P(B) = 2/5, and P(A∪B) = 3/5, then P(A∩B) = ?
(A) 4/15    (B) 11/15    (C) 1/3    (D) 2/5
36The number of ways to distribute 10 different prizes among 5 students is:
(A) 510    (B) 510    (C) 105    (D) 10!/5!
37The probability of drawing a king or a heart from a deck of cards is:
(A) 1/13    (B) 4/13    (C) 16/52    (D) 17/52
38If nP4 = 20 × nP2, then n = ?
(A) 5    (B) 7    (C) 8    (D) 10
39In how many ways can 5 men and 5 women be seated alternately in a row?
(A) 2 × 5! × 5!    (B) 2 × 5! × 5!    (C) 10!    (D) 5! × 5!
40If A and B are independent events with P(A) = 0.3 and P(B) = 0.4, then P(A'∩B') = ?
(A) 0.12    (B) 0.42    (C) 0.7    (D) 0.88
41The number of ways to arrange 5 rings on 4 fingers is:
(A) 54    (B) 45    (C) 20    (D) 120
42The probability that a number selected from 1 to 50 is a prime number is:
(A) 1/5    (B) 3/10    (C) 1/2    (D) 2/5
43If nC5 = nC11, then nC16 = ?
(A) 0    (B) 1    (C) 16    (D) n
44In how many ways can 10 students be divided into two groups of 5 each?
(A) 10!    (B) 126    (C) 252    (D) 512
45If P(A) = 0.6, P(B) = 0.3, and P(A∩B) = 0.2, then P(A|B') = ?
(A) 0.4    (B) 4/7    (C) 2/3    (D) 0.8
46The number of ways to select a committee of 5 from 7 men and 6 women with at least 3 men is:
(A) 756    (B) 756    (C) 1001    (D) 1287
47The probability of getting a total of 9 when two dice are thrown is:
(A) 1/9    (B) 1/9    (C) 1/6    (D) 5/36
48If n+2C8 : n-2P4 = 57:16, then n = ?
(A) 10    (B) 19    (C) 20    (D) 25
49In how many ways can the letters of the word "ARRANGE" be arranged?
(A) 1260    (B) 1260    (C) 2520    (D) 5040
50If P(A) = 1/4, P(B) = 1/3, and P(A∪B) = 1/2, then P(A'∩B') = ?
(A) 1/4    (B) 1/2    (C) 3/4    (D) 2/3
51The number of ways to select 3 vowels and 2 consonants from 5 vowels and 6 consonants is:
(A) 150    (B) 150    (C) 200    (D) 300
52The probability that a card drawn from a pack is either a king or a queen is:
(A) 1/13    (B) 2/13    (C) 3/13    (D) 4/13
53If nC4, nC5, nC6 are in AP, then n = ?
(A) 7    (B) 14    (C) 21    (D) 28
54In how many ways can 12 different books be distributed equally among 4 students?
(A) 12!    (B) 12!/(3!)4    (C) 412    (D) 124
55If two dice are thrown, the probability that the sum is divisible by 3 or 4 is:
(A) 1/3    (B) 5/9    (C) 2/3    (D) 7/9