1. Suppose a designer has a palette of 8 colors to work with and wants to design a flag with 3 vertical stripes, all of different colors. How many possible flags can be created?

2. In how many ways can 5 books be chosen from a group of nine? Your answer is :

3. A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 12 characters long, and that each character is either a lowercase letter, (a, b, c, etc.), an uppercase letter (A, B, C, etc.) or a numerical digit (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9). Assume that the hacker makes random guesses. What is the probability that the hacker guesses the password on his first try? Enter your answer as a decimal or a fraction, not a percentage.

4. At the ice cream shop, there are 23 flavors of ice cream available. How many ways can you select a bowl of 3 scoops of ice cream if each scoop is a different flavor? Your answer is :

The ice cream shop has 9 types of toppings available, and you decide to add 5 toppings to your bowl of 3 scoops of ice cream. How many combinations of 3 scoops of ice cream and 5 toppings are possible? Your answer is :