A computer password consists of six characters.  a) how many different passwords are possible if each character may be any lowercase letter or digit? b)  how many different passwords are possible if each character may be any lowercase letter or digit, and at least one character must be a digit? c) a computer system requires that passwords contain at least one digit. If seven characters are generated at random, and each is equally likely to be any of the 26 letters or 10 digits,what is the probability that a valid password will be generated?

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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A computer password consists of six characters. 

a) how many different passwords are possible if each character may be any lowercase letter or digit?

b)  how many different passwords are possible if each character may be any lowercase letter or digit, and at least one character must be a digit?

c) a computer system requires that passwords contain at least one digit. If seven characters are generated at random, and each is equally likely to be any of the 26 letters or 10 digits,what is the probability that a valid password will be generated?

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