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You are signing up to a website that requires you to create a username that is exactly 8 characters long. To create the username, you can use lowercase letters (a-z, 26 possible choices) and numerical digits (0-9, 10 possible choices). (a) First, suppose that you can choose any of those characters, as many times as you want (as long as the total number of characters is 8). How many usernames are possible? (b) There are five vowels (a,e,i,o,u) along with 21 consonants. Suppose that you decide to make up a password where the first seven characters alternate - consonant, vowel, consonant, vowel, consonant,

You are signing up to a website that requires you to create a username that is exactly 8 characters long. To create the username, you can use lowercase letters (a-z, 26 possible choices) and numerical digits (0-9, 10 possible choices). (a) First, suppose that you can choose any of those characters, as many times as you want (as long as the total number of characters is 8). How many usernames are possible? (b) There are five vowels (a,e,i,o,u) along with 21 consonants. Suppose that you decide to make up a password where the first seven characters alternate - consonant, vowel, consonant, vowel, consonant,

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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You are signing up to a website that requires you to create a username that is exactly 8 characters long. To create the username, you can use lowercase letters (a-z, 26 possible choices) and numerical digits (0-9, 10 possible choices). (a) First, suppose that you can choose any of those characters, as many times as you want (as long as the total number of characters is 8). How many usernames are possible? (b) There are five vowels (a,e,i,o,u) along with 21 consonants. Suppose that you decide to password where the first seven characters alternate - consonant, vowel, consonant, vowel, consonant, vowel - with repetitions allowed, and a digit as the eighth character. How many different passwords can be make up? up a (c) There are five vowels (a,e,i,o,u) along with 21 consonants. Suppose that we want to make up a password where the first character must be a vowel and the second character must be a consonant if and the last character must be an odd number. How many different password can be make there are no other restriction on the third, through seventh characters and repetitions is allowed. up (d) There are five vowels (a,e,i,o,u) along with 21 consonants. Suppose that we want to make up a password where the first character must be a vowel and the second character must be a consonant and the last character must be an odd number. How many different password can be make up if the only restriction on the third through seventh characters is that it has to be unique. (i.e no repeats)
Transcribed Image Text:You are signing up to a website that requires you to create a username that is exactly 8 characters long. To create the username, you can use lowercase letters (a-z, 26 possible choices) and numerical digits (0-9, 10 possible choices). (a) First, suppose that you can choose any of those characters, as many times as you want (as long as the total number of characters is 8). How many usernames are possible? (b) There are five vowels (a,e,i,o,u) along with 21 consonants. Suppose that you decide to password where the first seven characters alternate - consonant, vowel, consonant, vowel, consonant, vowel - with repetitions allowed, and a digit as the eighth character. How many different passwords can be make up? up a (c) There are five vowels (a,e,i,o,u) along with 21 consonants. Suppose that we want to make up a password where the first character must be a vowel and the second character must be a consonant if and the last character must be an odd number. How many different password can be make there are no other restriction on the third, through seventh characters and repetitions is allowed. up (d) There are five vowels (a,e,i,o,u) along with 21 consonants. Suppose that we want to make up a password where the first character must be a vowel and the second character must be a consonant and the last character must be an odd number. How many different password can be make up if the only restriction on the third through seventh characters is that it has to be unique. (i.e no repeats)
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