Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 6 - Section 6.1 - The Basics of Counting - Exercises - Page 396: 18

Answer

a) 256 b) 64 c) 32 d) 243

Work Step by Step

A DNA sequence is a sequence of letters, each of which is one of A, C, G, or T. Thus by the product rule there are $4^5$ RNA sequences of length five if we impose no restrictions. a)If the last letter is specified to be A, then we get to choose only four letters, rather than five, so the answer $4^4$=256. b)If the two letters are specified, first is T and last is G, then we get to choose only three letters, rather than five, so the answer if $4^3$=64. c)If only A or T is allowed in each position, then there are just two choices at each of five stages, so the answer is $2^5$ = 32. d)If C is excluded, then each position can be chosen from among three letters, rather than four. Therefore, the answer is $3^5$=243.
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