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in this question, you may leave your answer in unevaluated form. For example, answers may be written as P(52, 5), 52°, 52!, etc.). A website requires users to use five character passwords made up of the lower case letters, upper case letters, and the eight symbols !, ?, @, #, $, %, &, and * (so there are 60 characters in total that may be used). How many possible passwords are there (a) in total (if there are no additional restrictions on passwords)? (b) if characters may not be used more than once? (c) if exactly one capital letter must be used (and characters may be used more than once)?

in this question, you may leave your answer in unevaluated form. For example, answers may be written as P(52, 5), 52°, 52!, etc.). A website requires users to use five character passwords made up of the lower case letters, upper case letters, and the eight symbols !, ?, @, #, $, %, &, and * (so there are 60 characters in total that may be used). How many possible passwords are there (a) in total (if there are no additional restrictions on passwords)? (b) if characters may not be used more than once? (c) if exactly one capital letter must be used (and characters may be used more than once)?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(Note: in this question, you may leave your answer in unevaluated form. For example, answers may be written as P(52, 5), 52°, 52!, etc.). A website requires users to use five character passwords made up of the lower case letters, upper case letters, and the eight symbols !, ?, @, #, $, %, &, and (so there are 60 characters in total that may be used). How many possible passwords are there (a) in total (if there are no additional restrictions on passwords)? (b) if characters may not be used more than once? (c) if exactly one capital letter must be used (and characters may be used more than once)? (d) if at least one capital letter must be used (and characters may be used more than once)?
Transcribed Image Text:(Note: in this question, you may leave your answer in unevaluated form. For example, answers may be written as P(52, 5), 52°, 52!, etc.). A website requires users to use five character passwords made up of the lower case letters, upper case letters, and the eight symbols !, ?, @, #, $, %, &, and (so there are 60 characters in total that may be used). How many possible passwords are there (a) in total (if there are no additional restrictions on passwords)? (b) if characters may not be used more than once? (c) if exactly one capital letter must be used (and characters may be used more than once)? (d) if at least one capital letter must be used (and characters may be used more than once)?
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