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This set of Probability and Statistics Multiple Choice Questions & Answers (MCQs) focuses on “Permutations and Combinations”. 1. If 16Pr-1 : 15Pr-1 = 16 : 7 then find r. a) 10 b) 12 c) 7 d) 8 View Answer Answer: a Explanation: We know that \(^nP_r = \frac{n!}{(n-r)!} \) Hence \(^{16}P_{r-1} : \, ^{15}P_{r-1} = 16 : 7 \) \([\frac{16!}{16-(r-1)!}] ÷ [\frac{15!}{15-(r-1)}] = 16 ÷ 7 \) 16 ÷ (17 – r) = 16 ÷ 7 17 – r = 7 Hence r = 10. 2. In a colony, there are 55 members. Every member posts a greeting card to all the members. How many greeting cards were posted by them? a) 990 b) 890 c) 2970 d) 1980 View Answer Answer: c Explanation: First player can post greeting cards to the remaining 54 players in 54 ways. Second player can post greeting card to the 54 players. Similarly, it happens with the rest of the players. The total numbers of greeting cards posted are 54 + 54 + 54 … 54 (55times) = 54 x 55 = 2970. 3. Find the number of ways of arranging the letters of the words DANGER, so that no vowel occupies odd place. a) 36 b) 48 c) 144 d) 96 View Answer Answer: c 4. Find the sum of all four digit numbers that can be formed by the digits 1, 3, 5, 7, 9 without repetition. a) 666700 b) 666600 c) 678860 d) 665500 View Answer Answer: b Explanation: The given digits are 1, 3, 5, 7, 9 Sum of r digit number= n-1Pr-1 (Sum of all n digits)×(1111… r times) N is the number of non zero digits. Here n=5, r=4 The sum of 4 digit numbers4P3 (1+3+5+7+9)(1111)=666600. 5. If nPr = 3024 and nCr = 126 then find n and r. a) 9, 4 b) 10, 3 c) 12, 4 d) 11, 4 View Answer Answer: a Explanation: \(\frac{^nP_r}{^nC_r} = \frac{3024}{126} \) \(^nP_r = \frac{n!}{(n-r)!} \) \(^nC_r = \frac{n!}{(n-r)!×r!} \) Hence \( [\frac{n!}{(n-r)!}]÷[\frac{n!}{(n-r)!×r!}] \) = 24 24 = r! Hence r = 4 Now nP4 = 3024 n = 9.
Check this: Engineering Mathematics MCQ | Numerical Methods MCQ 6. Find the number of rectangles and squares in an 8 by 8 chess board respectively. a) 296, 204 b) 1092, 204 c) 204, 1092 d) 204, 1296 View Answer Answer: b 7. There are 20 points in a plane, how many triangles can be formed by these points if 5 are colinear? a) 1130 b) 550 c) 1129 d) 1140 View Answer Answer: a Explanation: Number of points in plane n = 20. Number of colinear points m = 5. Number of triangles from by joining n points of which m are colinear = nC3 – mC3 Therefore the number of triangles = 20C3 – 5C3 = 1140-10 = 1130. 8. In how many ways can we select 6 people out of 10, of which a particular person is not included? Answer: c 9. Number of circular permutations of different things taken all at a time is n!. a) True b) False View Answer Answer: b 10. Is the given statement true or false? View Answer Answer: a \(^nC_{n-r} = \frac{n!}{r!×(n-r)!} = ^nC_r. \) Sanfoundry Global Education & Learning Series – Probability and Statistics. To practice all areas of Probability and Statistics, here is complete set of 1000+ Multiple Choice Questions and Answers.
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn. Subscribe to his free Masterclasses at Youtube & technical discussions at Telegram SanfoundryClasses.
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