1. Suppose there are 30 rooms. Find the number of outcomes for following problems:

a) Prof. Xin wants to choose one room for MAT100 class

b) Prof. Xin wants to choose any two rooms

c) Prof. Xin wants to choose one room for MAT100 and choose one room for MAT150

2. An apartment complex offers apartments with four different options, designated by A through D.

A. One bedroom, Two Bedrooms or Three Bedrooms

B. One Bathroom or Two Bathrooms

C. First Floor or Second Floor

D. Lake View, Golf Course View, or No Special View

How many apartment options are available?

3.

Give f(n) = 2f(n 1) (n 2), (0) = 1, and f(1) = 2, find (4).