# A how many ways are there to choose committees

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the following questions. (a) How many ways are there to choose committees consisting of four members of the club? (b) How many ways are there to choose a president, vice president, secretary, and treasurer of the club? (c) How many ways are there to choose committees consisting of four people if exactly three of the four must be female? (d) How many ways are there to choose committees consisting of four people if none of them can be female? (e) How many ways are there to choose committees consisting of four people if at least one must be female. 8. (5 pts.) (a) The following proposition represents an invalid argument form: [¬p (p q)] ¬q. What is the name of the popular fallacy given by the proposition above? (b) The following proposition represents an invalid argument form: [q (p q)] p. What is the name of the popular fallacy given by the proposition above? (c) Why is reasoning using either of the argument forms found in (a) or (b) deemed invalid?

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MAD2104/Final Exam Page 4 of 8 9. (5 pts.) Label each of the following assertions with "true" or "false". Be sure to write out the entire word. (a) The set of all subsets of the natural numbers is countable. (b) The number of functions from a set with 8 elements to a set with 15 elements is P(15,8). (c) The coeffient of x 4 y 5 in the expansion of (x + y) 9 is the number of 5 element subsets of an 9 element set. (d) There is a one-to-one correspondence between the natural numbers and the rational numbers. (e) The total number of ways to assign truth values to five true-false problems by using the letters T and F is given by the sum below.
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