Consider strings of length n, n ≥ 1, over the set (a, b, c, d). (a) How many such strings contain at least one pair of adjacent characters that are the same? (Hint: Any of the four letters may be chosen for the first character. For each subsequent character, any letter except the one directly to its left may be chosen.) 8 x (b) If a string of length eight over (a, b, c, d) is chosen at random, what is the probability that it contains at least one pair of adjacent characters that are the same? (Round your answer to the nearest tenth of a percent.)
Consider strings of length n, n ≥ 1, over the set (a, b, c, d). (a) How many such strings contain at least one pair of adjacent characters that are the same? (Hint: Any of the four letters may be chosen for the first character. For each subsequent character, any letter except the one directly to its left may be chosen.) 8 x (b) If a string of length eight over (a, b, c, d) is chosen at random, what is the probability that it contains at least one pair of adjacent characters that are the same? (Round your answer to the nearest tenth of a percent.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Consider strings of length n, n ≥ 1, over the set {a, b, c, d}.
(a) How many such strings contain at least one pair of adjacent characters that are the same? (Hint: Any of the four letters may be chosen for the first character. For each subsequent character, any letter except the one directly to its left may be chosen.)
8
×
(b) If a string of length eight over {a, b, c, d} is chosen at random, what is the probability that it contains at least one pair of adjacent characters that are the same? (Round your answer to the nearest tenth of a percent.)
86.7
%](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3cf874b-7a7b-478f-a7b8-421442e72224%2F6800fe90-9b10-45ff-ba50-12d4c1512b56%2Fwnc76co_processed.png&w=3840&q=75)
Transcribed Image Text:Consider strings of length n, n ≥ 1, over the set {a, b, c, d}.
(a) How many such strings contain at least one pair of adjacent characters that are the same? (Hint: Any of the four letters may be chosen for the first character. For each subsequent character, any letter except the one directly to its left may be chosen.)
8
×
(b) If a string of length eight over {a, b, c, d} is chosen at random, what is the probability that it contains at least one pair of adjacent characters that are the same? (Round your answer to the nearest tenth of a percent.)
86.7
%
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