(a) Suppose your student ID number is 2 letters followed by 3 numbers (e.g. AA111). How many unique student ID numbers are possible?

(b)If you change the student ID rules (from part (a)) so that

:The first two letters must be different (U W is okay but D D is not).

All three numbers must be different, and the first number cannot be 0 (so 497 is okay, but 032and 199 are not).

how many student ID numbers are possible?

(c) A large group of 10 people are going to a movie, and they take over a row in the theater with 10seats. How many ways could they be arranged in the row?

(d)At an ice cream parlor you can choose 3 flavors of ice cream (from 10) and 3 toppings (from 20) .How many different combinations are there?

(e)Suppose you have 3 red marbles, 3 blue marbles, and 3 green marbles, all lined up like.How many unique arrangements could you make of these 9 marbles, assuming marbles of the same color are indistinguishable?

2.A typical computer keyboard can make 94 characters (all letters and numbers, upper and lower case, and other symbols). Let's use this to determine how secure a password is.

(a)If your UH password needs to be 10 characters long, how many unique passwords are possible?

(b) Usually passwords have additional requirements; no character can be repeated, and you cannot use these four symbols{ } \ /. With these new rules, how many passwords are now possible?

(c)If you had a computer that could check 1,000,000 passwords each second, how long would it take to check every password in part (b)? Write the answer in years, and can be approximate. What does this tell you about?

3.This problem will ask you to come up with examples of experiment/events with a given probability. I'm asking about classical probability only; your subjective opinion probability will not count here. You must also explain why your event has the given probability - if you don't justify with acalculation or explanation.

(3A). An event with probability 1.

(3B). An event with probability 0

(3C). An event with probability 0.5

(3D). An event with probability16

(3E). An event with probability 7/8.