Passwords of length 10 are formed using the character set S = {a, b, c, …,...

Passwords of length 10 are formed using the character set S = {a, b, c, …, z, A, B, …, Z, 0, 1, 2, .., 9}. Thus the set S consists of 62 different characters. For each part below, you must include a few words that describe your counting strategy.
(a) How many passwords of length 10 use the character Q exactly two times?
(b) How many passwords of length 10 use at most one of the “upper case” letters (the A, B, …, Z letters)?
(c) How many passwords of length 10 repeats at least one character?
(d) How many passwords of length 10 repeats at least one character and also include the character M at least
once?

Solutions

Expert Solution

a) The number of passwrods of length 10 that use the character Q exactly two times here is computed here as:
= Number of ways to select 2 positions from the 10 positions which will have Q * Number of ways to choose from 61 letters for each of the remaining 8 positions

b) The number of passwords of length 10 that use at most one of the “upper case” letters (the A, B, …, Z letters) is computed here as:
= Number of passwords that dont use the “upper case” letters (the A, B, …, Z letters) + Number of passwords that use exactly 1 “upper case” letters (the A, B, …, Z letters)

c) The number of passwrods of length 10 that repeats at least one character here is computed as:

= Total number of passwords possible - Number of passwords with no character repetition

d) Now the number of passwords of length 10 that repeats at least one character and also include the character M at least once is computed here as:

= Total number of passwords of length 10 that repeats at least one character - Total number of passwords of length 10 that repeats at least one character and dont have an M

This is the required expression here.

orchestra answered 1 year ago

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