Homework 01

This homework follows the standard late penalty: 0% if in the stat310 mailbox by Thursday 19 Jan 4pm, 10% by 5pm the following day, 100% otherwise. Please read the syllabus for other homework policies.

  1. (8 pts) License plates in Texas

    1. (2 pts) License plates in Texas are made up of two letters followed by a number followed by a letter and three numbers (eg. BB1 B001). How many possible plates are there?

    2. (2 pts) Some letter combinations are reserved for various purposes. AA0-A001 to AZ9-Z999 and XA0-A001 to XZ0-Z999 are reserved for non-passenger vehicles. How many passenger license plates are available?

    3. (2 pts) An additional restriction is that no number plate can start with any of the following two letter combinations: BS - DR - FC - FK - FU - HS - MD - PP - PU - SN - UN - VD - VP - VT. How many passenger plates does that leave?

    4. (2 pts) Is this a good system or not? Why?

  2. (10 pts) Eating at chipotle

    Chipotle menu
    (Click for full sized version)

    1. (3 pts) How many different burritos can you make with the order form above? Assume that except where specified, you can have as many (or as few) elements from a class (rice, beans, fajita veg, meat, salsa, dairy, guacamole, lettuce) as you like.

    2. (3 pts) How many different burritos can you make if you assume you must choose at most one element from each class?

    3. (2 pts) You are getting a Burrito for your friend, but you completely forgot what order he wants besides the fact he wants Steak and you know he hates salsa. What is probability that you randomly pick the right order?

    4. (2 pts) How many different vegan meals (no meat or dairy) can you create at chipotle? (Assume at most 1 selection from each category)

  3. (4 pts) Set theory warm-up.

    For each question, draw a venn diagram that illustrates the set, then simplify the expression as much as possible. (1/2 pt each question)

    1. \( A \cup B \)
    2. \( A \cup B^\complement \)
    3. \( A^\complement \cup B^\complement \)
    4. \( (A \cap B)^\complement \)
    5. \( (A^\complement \cap B^\complement)^\complement \)
    6. \( (A \cap B) \cup (A \cap C) \)
    7. \( (A \cup B) \cap (A \cup C) \)
    8. \( (A \cap A) \cup (B \cup B) \)