a. Solve this problem and clearly write up your solution: A programmer designed a new program that required the user to enter a three-character password in order to be recognized as a legal user. The first character must be a W or K. The second character must be a number: 1, 2, 3, 4, 5.
The third character must be a symbol selected from $, %, *. How many possible passwords can be created for this program? What is the probability of guessing the password on the first try?
b. Describe your work on this problem considering each of the following:
● Problem Solving: Do you consider this task a problem? Why or why not?
● Reasoning and Proof: Did your solution provide proof that your solution is correct?
● Communication: How did you communicate your solution? Did you use multiple ways to explain your solution? Listen or read another student’s solution to the problem. Was it communicated in the manner you communicated your solution?
● Connections: Connect this problem with another mathematical idea. Connect this problem with another problem outside of mathematics.
● Representations: Show a solution to the problem in more than one way. Describe how you used different representations in these ways.
3. Make a list of as many different representations for the number 75 as you can think of. Compare your list with the lists of others. You might use equivalent expressions, models, words, pictures, and so on. It is a sign of flexibility in thinking to be able to represent numbers and other mathematical ideas in many different ways. 4. What are the three distinct types of connections that are important in school mathematics? Give two examples of each type of connection