8, Assignment Math 240, Fall 2005
Due: 2:45pm, October 11. Value: 30 pts. On all questions, here and elsewhere, you can feel free to express answers as a simple expression without writing down the specic number; for example, if the answer is 2 100 C(100, 3), you can write that rather than attempt to compute the number. However, your answer should always be as simple as possible, and it should always involve only well-known mathematical functions. In all cases, you should justify your answer: Never write just a number or an expression. Without a justication, I will give you zero credit, even if the answer is correct.
Based on September 29 material (4.1)
Problem A. How many strings of n bits are there where every 1 bit is followed by a 0 bit? Problem B. How many strings of 10 bits have either 0 bits in the rst, third, fth, seventh, ninth and places, or 0 bits in the rst, fourth, seventh, and tenth places. Problem C. Suppose we have a set of six tiles labeled as listed below. How many different six-letter strings can be formed using the tiles? a. b. O,H,D,E,A,R. O,H,D,E,E,R. (Hint: Think about the list of all possible orderings, and think about how often an ordering is a duplicate of another.)
Based on October 4 material (4.2)
Problem D. 4.2 (p 319): 8. Problem E. 4.2 (p 319): 32. Problem F. 4.2 (p 319): 36. Knowing is mutual; that is, if I know somebody, then that person also knows me.
Based on October 6 material (4.3)
Problem G. How many strictly increasing sequences of three integers between 1 and 100 (inclusive) are there? Problem H. 4.3 (p 325): 26abc. In parts a and c, take the eld means that we dont care which positions the individual players take.