CompSci 102 Discrete Mathematics for CSSpring 2005 Forbes In-class Questions 41. Prove that a knight starting at (0, 0) can visit every square on the unbounded negativequadrant.1Sum and Product Rule2. At University X, there are 19 CS majors, 17 math majors, 11 Poli Sci majors, and 8 Econmajors. Having multiple majors is not allowed at X.(a) How many ways are there ot choose someone who is either a CS major or a math major?(b) The total number of students at X is?(c) How m any different ways are there to pick four students with different majors fromamong the students at University X?3. How many ways are there to deal a 5-card sequence from a 52 card poker deck?4. How many ways are there to select an ordered pair of numbers from 1 to 7 (repetition allowed)so that the sum is even? Think of it as counting black squares on a checkerboard. (Why?)Division Rule5. Suppose that 800 pieces of candy are to be sold 50 pieces to a box. How many boxes arerequired?6. How many ways are there to 2-color a a 2-by-2 checkerboard? How many equivalence classesare there under reflection and rotation?CompSci 102, Spring 2005, In-class Questions 4 2Inclusion-Exclusion7. Count the number of bit-strings of length 8 that have either 1 as a prefix or 00 as a suffixTree Diagrams8. Count the subsets of 2, 5, 11, 17, 23 whose sum is at most 29.CompSci 102, Spring 2005, In-class Questions 4
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