1. A club has 25 members. i. Number of ways to choose four members of the club to serve on an executive committee? ii. Number of ways to choose a president, vice president, secretary, and treasurer of the club, where no person can hold more than one off

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."