You are asked to create a 4​-character ​password, and each character may be any of the 26 letters of the alphabet or the 10 numerals 0 through 9. How many different passwords are​ possible? Explain your reasoning. A) 364, because there are 26 + 10 = 36 different characters to choose from, so there are 364 different arrangements possible. B) 36, because there are 26 + 10 = 36 different arrangements of characters. C) 36, because there are 26 + 10 = 36 different characters to choose from. D) 264 + 104, because there are 264 different letters to choose from and 104 different numerals to choose from. E) 264 + 104, because there are 264 different arrangements of the letters and 104 different arrangements of the numerals 0 through 9.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 36SE: The number of 5-element subsets from a set containing n elements is equal to the number of 6-element...
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You are asked to create a 4​-character ​password, and each character may be any of the 26 letters of the alphabet or the 10 numerals 0 through 9. How many different passwords are​ possible? Explain your reasoning.

A) 364, because there are 26 + 10 = 36 different characters to choose from, so there are 364 different arrangements possible.

B) 36, because there are 26 + 10 = 36 different arrangements of characters.

C) 36, because there are 26 + 10 = 36 different characters to choose from.

D) 264 + 104, because there are 264 different letters to choose from and 104 different numerals to choose from.

E) 264 + 104, because there are 264 different arrangements of the letters and 104 different arrangements of the numerals 0 through 9.

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