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20. Georgette labels her notebooks with a string of three letters from the set {A,B,X,Y,Z}, and the first two letters in each label must be distinct. (Acceptable: АВА, ХҮА. Unacceptable:AAХ, ВВВ.) Нow many different labels are there? (а) 10 (b) 60 (c) 14 (d) 100 (е) 125 (f) none of the above

20. Georgette labels her notebooks with a string of three letters from the set {A,B,X,Y,Z}, and the first two letters in each label must be distinct. (Acceptable: АВА, ХҮА. Unacceptable:AAХ, ВВВ.) Нow many different labels are there? (а) 10 (b) 60 (c) 14 (d) 100 (е) 125 (f) none of the above

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Please answer #20 and explain your reasoning!

**Question 19: Coin Toss Probability** An unfair coin with Pr[H] = 0.9 is tossed (independently) 5 times. What is the probability that the first, third, and fifth tosses are H, and all the others are T? Options: - (a) 0.0243 - (b) 0.00243 - (c) 0.243 - (d) 0.0729 - (e) 0.00729 - (f) none of the others **Question 20: Notebook Labeling** Georgette labels her notebooks with a string of three letters from the set {A, B, X, Y, Z}, and the first two letters in each label must be distinct. (Acceptable: ABA, XYA. Unacceptable: AAX, BBB.) How many different labels are there? Options: - (a) 10 - (b) 60 - (c) 14 - (d) 100 - (e) 125 - (f) none of the above **Question 21: Multiple Choice Exam** A multiple-choice exam consists of 4 questions. Each question has 5 possible answers, exactly one of which is correct. Prstč decides to pick the answer to each question at random. What is the probability that he will get precisely two correct answers? Options: - (a) 0.1024 - (b) 0.9744 - (c) 0.2048 - (d) 0.1536 - (e) 0.0256 - (f) none of the above
Transcribed Image Text:**Question 19: Coin Toss Probability** An unfair coin with Pr[H] = 0.9 is tossed (independently) 5 times. What is the probability that the first, third, and fifth tosses are H, and all the others are T? Options: - (a) 0.0243 - (b) 0.00243 - (c) 0.243 - (d) 0.0729 - (e) 0.00729 - (f) none of the others **Question 20: Notebook Labeling** Georgette labels her notebooks with a string of three letters from the set {A, B, X, Y, Z}, and the first two letters in each label must be distinct. (Acceptable: ABA, XYA. Unacceptable: AAX, BBB.) How many different labels are there? Options: - (a) 10 - (b) 60 - (c) 14 - (d) 100 - (e) 125 - (f) none of the above **Question 21: Multiple Choice Exam** A multiple-choice exam consists of 4 questions. Each question has 5 possible answers, exactly one of which is correct. Prstč decides to pick the answer to each question at random. What is the probability that he will get precisely two correct answers? Options: - (a) 0.1024 - (b) 0.9744 - (c) 0.2048 - (d) 0.1536 - (e) 0.0256 - (f) none of the above
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