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In how many different ways can five elements be selected in order from
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1.A club has 25 members.How many ways are there to choose four members of the club to serve on an executive committee?How many ways are there to choose a president, vice president, secretary, and treasurer of the club, where no person can hold more than one office?

2.In how many different ways can five elements be selected in order from a set with three elements when repetition is allowed?

3.What is the probability that a fair die never comes up an even number when it is rolled six times?

(Note: Enter the value of probability in decimal format and round it to three decimal places.)

4.Let p and q be the propositions

p :You have the flu.

q :You miss the final examination.

Identify the English sentence that expresses the compound proposition p → q.

5. Let q and r be the propositions

q :You miss the final examination.
r :You pass the course.

The English sentence of the compound proposition ¬q ↔ r is "You do not miss the final exam if and only if you pass the course."

6.)Let q and r be the propositions

q :You miss the final examination.
r :You pass the course.

The English statement for the compound proposition q → ¬r is "If you miss the final exam, then you pass the course."

7.)Let p, q, and r be the propositions
p :You have the flu.
q :You miss the final examination.
r :You pass the course.

Identify the statement that express the compound proposition p  q  r as an English sentence.

8.)Let p, q, and r be the propositions
p :You have the flu.
q :You miss the final examination.
r :You pass the course.

Identify the English sentence of the compound proposition (p → ¬r)  (q → ¬r).

9.Let p, q, and r be the propositions
p :You have the flu.
q :You miss the final examination.
r :You pass the course.

The English sentence of the compound proposition (p  q)  (¬q  r) is "Either you have the flu and miss the final exam, or you do not miss the final exam and do pass the course."

10.) True or False :The negation of the statement "Kwame will take a job in industry or go to graduate school." using De Morgan's law is "Kwame will not take a job in industry or will not go to graduate school."

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