1.A witness to a hit-and-run accident tells the police that the license plate of the car in the accident, which contains three letters followed by three digits, starts with the letter A and contains both the digits 1 and 2. How many different license plates can fit this description?
Discrete Structure Questions
1.A witness to a hit-and-run accident tells the police that the license plate of the car in the accident, which contains three letters followed by three digits, starts with the letter A and contains both the digits 1 and 2. How many different license plates can fit this description?
2.If someone is lying, who copied the assignment?
Alex: Cate copied the assignment.
Cate: David copied the assignment.
David: Cate is lying.
Keil: I didn't copy.
3. Let ?(?) be the statement that 13 + 23 + 33 +⋯+ ?3 = ((?(?+1))/2)2 for the positive integer n.
a) What is the statement ?(1)?
b) What is the inductive hypothesis?
c) What do you need to prove in the inductive step?
d) Complete the inductive step, identifying where you use the inductive hypothesis.
4.Suppose that the number of bacteria in a colony triples every hour.
a) Set up a recurrence relation for the number of bacteria after n hours have elapsed.
b) If 100 bacteria are used to begin a new colony, how many bacteria will be in the colony in 10 hours?
5.Pelin has two coolers. The first contains eight cans of cola and three cans of lemonade. The second coller contains five cans of cola and seven cans of lemonade. Pelin randomly selects one can from the first cooler and puts it into the second cooler. Five minutes later Beril randomly selects two cans from the second cooler. If both of Beril’s selections are cans of cola, what is the probability Pelin initially selectes a can of lemonade?
6. For each course at a university, there may be one or more other courses that are its prerequisites. How can a graph be used to model these courses and which courses are prerequisites for which courses? Should edges be directed or undirected? Looking at the graph model, how can we find courses that do not have any prerequisites and how can we find courses that are not the prerequisite for any other courses?
7.Determine the existence of Euler and/or Hamilton circuits/paths. If your answer is “yes”, please write the circuit and/or path (added image)
8.Solve the traveling salesman problem for this graph by finding the total weight of all Hamilton circuits and determining a circuit with minimum total weight. (added image)
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