A password is a sequence of five characters. Each character is one of twenty-six uppercase letters...

A password is a sequence of five characters. Each character is one of twenty-six uppercase letters (“A” through “Z”), one of ten digits (“0” through “9”), or one of five symbols (“+”, “-”, “!”, “<”, “>”). Count the number of possible passwords that can be created in each of the following scenarios. Consider each part of this questions separately.

(a) There are no restrictions on how the characters are chosen.

(b) A password must begin with a letter and end with a symbol.

(c) A password must contain two letters, two digits, and one symbol (a letter and/or digit can be reused).

(d) Re-solve Part (c), if the two letters must be different and the two digits must be different.

(e) A password must contain exactly two different characters.

2.) A symposium schedule will consist of twelve speakers. Seven speakers are from industry, three speakers are from academia, and two speakers are from the government. For scheduling purposes, speakers of the same type are considered indistinguishable.

(a) In how many ways can the speaker schedule be arranged?

(b) Re-solve Part (a) if the first and last speakers must be of the same type (i.e., both from industry, both from academia, or both from government)?

Expert Solution

orchestra answered 1 year ago

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