## Homework 2

Homework 2 is due on Monday, May 31st.

1. Read Chapter 4. Indicating in at most three sentences one or more of the following: the passage in the reading— including its page number—you:

• Found most difficult
• Found most surprising
• Would like to have discussed in the next lectur

2. To successfully complete a B.S. degree in CISE, students must satisfy the following requirements:

• Complete at least 5 of 10 core courses.
• Complete at least 72 credit hours.

Know that each course worths 3 credit hours and there are 20 optional coures. A student plans to complete the degree with minimum number of credit hours. How many choice does he have, no matter the order of selected courses.

3. Seven darts are thrown onto a circular dartboard of radius 10 units. Can we show that there will always be two darts  which are at most 10 units apart?

4. Lattice paths are paths in the plane from (0, 0) to (x, y) (x, y are integers) where at each step you must move either one unit up or one unit right. Count the number of lattice paths from (0, 0) to (x, y).

5. How many 9-digit numbers are there if each has exactly one 5 digit and a 4 digit?