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.
| 01 | The value of nPr is: (A) n!/(n-r)! (B) n!/r!(n-r)! (C) n!/r! (D) (n-r)!/n! |
| 02 | The value of nCr is: (A) n!/(n-r)! (B) n!/r!(n-r)! (C) n!/r! (D) r!/n!(n-r)! |
| 03 | If nC8 = nC12, then n = ? (A) 10 (B) 20 (C) 18 (D) 25 |
| 04 | How many 3-digit numbers can be formed using digits 1,2,3,4,5 without repetition? (A) 24 (B) 60 (C) 120 (D) 125 |
| 05 | The probability of getting a head when tossing a fair coin is: (A) 0 (B) 1/2 (C) 1 (D) 2 |
| 06 | If nPr = 720 and nCr = 120, then r = ? (A) 2 (B) 3 (C) 4 (D) 5 |
| 07 | In how many ways can 5 people sit in a row? (A) 25 (B) 120 (C) 60 (D) 240 |
| 08 | The probability of an impossible event is: (A) 0 (B) 1 (C) 1/2 (D) ∞ |
| 09 | If nC2 = 45, then n = ? (A) 8 (B) 10 (C) 9 (D) 11 |
| 10 | How many words can be formed from the letters of the word "MATHS"? (A) 24 (B) 120 (C) 60 (D) 720 |
| 11 | The probability of getting a prime number when a die is thrown is: (A) 1/2 (B) 1/2 (C) 2/3 (D) 1/3 |
| 12 | Number of diagonals in a hexagon is: (A) 6 (B) 9 (C) 12 (D) 18 |
| 13 | If 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 |
| 14 | In how many ways can 4 books be arranged on a shelf? (A) 16 (B) 24 (C) 12 (D) 8 |
| 15 | The value of 0! is: (A) 1 (B) 0 (C) ∞ (D) Not defined |
| 16 | If P(A) = 0.6, then P(A') = ? (A) 0.4 (B) 0.4 (C) 0.6 (D) 0.3 |
| 17 | How many triangles can be formed from 8 non-collinear points? (A) 56 (B) 56 (C) 28 (D) 64 |
| 18 | The 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 |
| 19 | If nP3 = 60, then n = ? (A) 4 (B) 5 (C) 6 (D) 7 |
| 20 | In 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 |
| 21 | If 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 |
| 22 | The number of ways to arrange the letters of the word "BANANA" is: (A) 720 (B) 60 (C) 120 (D) 360 |
| 23 | If 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 |
| 24 | How 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 |
| 25 | The probability of getting at least one head when two coins are tossed is: (A) 1/4 (B) 1/2 (C) 3/4 (D) 1 |
| 26 | If nCr = nCr+1, then nCr-1 = ? (A) nCr (B) n+1Cr (C) n-1Cr (D) nCr+2 |
| 27 | In how many ways can 6 people be seated around a circular table? (A) 720 (B) 120 (C) 60 (D) 360 |
| 28 | The probability that a leap year has 53 Sundays is: (A) 1/7 (B) 2/7 (C) 3/7 (D) 4/7 |
| 29 | If 15Cr = 15Cr+3, then r = ? (A) 3 (B) 6 (C) 9 (D) 12 |
| 30 | How many words can be formed from the letters of the word "COMMITTEE"? (A) 362880 (B) 45360 (C) 90720 (D) 22680 |
| 31 | If 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 |
| 32 | The number of ways to select a cricket team of 11 from 15 players is: (A) 15! (B) 1365 (C) 32760 (D) 39916800 |
| 33 | If three coins are tossed, the probability of getting exactly two heads is: (A) 1/8 (B) 3/8 (C) 1/2 (D) 5/8 |
| 34 | In how many ways can 4 red and 3 blue balls be arranged in a row? (A) 7! (B) 35 (C) 840 (D) 5040 |
| 35 | If 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 |
| 36 | The number of ways to distribute 10 different prizes among 5 students is: (A) 510 (B) 510 (C) 105 (D) 10!/5! |
| 37 | The 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 |
| 38 | If nP4 = 20 × nP2, then n = ? (A) 5 (B) 7 (C) 8 (D) 10 |
| 39 | In 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! |
| 40 | If 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 |
| 41 | The number of ways to arrange 5 rings on 4 fingers is: (A) 54 (B) 45 (C) 20 (D) 120 |
| 42 | The 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 |
| 43 | If nC5 = nC11, then nC16 = ? (A) 0 (B) 1 (C) 16 (D) n |
| 44 | In how many ways can 10 students be divided into two groups of 5 each? (A) 10! (B) 126 (C) 252 (D) 512 |
| 45 | If 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 |
| 46 | The 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 |
| 47 | The 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 |
| 48 | If n+2C8 : n-2P4 = 57:16, then n = ? (A) 10 (B) 19 (C) 20 (D) 25 |
| 49 | In how many ways can the letters of the word "ARRANGE" be arranged? (A) 1260 (B) 1260 (C) 2520 (D) 5040 |
| 50 | If 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 |
| 51 | The 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 |
| 52 | The 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 |
| 53 | If nC4, nC5, nC6 are in AP, then n = ? (A) 7 (B) 14 (C) 21 (D) 28 |
| 54 | In how many ways can 12 different books be distributed equally among 4 students? (A) 12! (B) 12!/(3!)4 (C) 412 (D) 124 |
| 55 | If 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 |
