Q1. This problem involves 8-digit binary strings such as 10011011 or 00001010.How many such strings are there?How many such strings end in 0?How many such strings have 1’s for their second and fourth digits?How many such strings have 1’s for their second or fourth digits?

Answer for sub question 1: The given task can be broken down into 8 sub tasks where the ith task Ti…

Answered: 1. This problem involves 8-digit binary…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.CT: Chapter Test

Problem 3CT: An Internet service provider requires its customer to select a password consisting of four letters...

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Suppose that the check digit is computed as described in Example . Prove that transposition errors of adjacent digits will not be detected unless one of the digits is the check digit. Example Using Check Digits Many companies use check digits for security purposes or for error detection. For example, an the digit may be appended to a -bit identification number to obtain the -digit invoice number of the form where the th bit, , is the check digit, computed as . If congruence modulo is used, then the check digit for an identification number . Thus the complete correct invoice number would appear as . If the invoice number were used instead and checked, an error would be detected, since .
An Internet service provider requires its customer to select a password consisting of four letters followed by three digits. Find how many such passwords are possible in each of the following cases: a Repetition of letters and digits is allowed. b Repetition of letters and digits is not allowed.
a. Excluding the identity cipher, how many different translation ciphers are there using an alphabet of n "letters"? b. Excluding the identity cipher, how many different affine ciphers are there using an alphabet of n "letters," where n is a prime?

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1. This problem involves 8-digit binary strings such as 10011011 or 00001010. How many such strings are there? How many such strings end in 0? How many such strings have 1’s for their second and fourth digits? How many such strings have 1’s for their second or fourth digits?