# Weekly note 8

This week cover counting in Chapter 4. We will look at the basic rules in section 4.1, permutations and combinations in section 4.3 and start with the binomial coefficients in section 4.4.

Below are 5 excercises that you are to solve and turn in to your section teacher before noon monday october 24th. Remember to mark your solutions with the number of your section and the name of the section teacher. Also below are few extra excercises that you can use to practice on and make sure that you have understood the material. Some of them will be solved in the sections if there is time.

## Homework 7

1. Exercise 22 in section 3.3 on page 254 in the textbook.

2. [Exam 2004]
1. Use induction to prove the equation for all natural numbers n.
2. Let the integers x1, x2, ..., xn all be odd numbers. Prove that the multiplication of all of them, i.e. the integer x1*x2* ...*xn, is an odd number.

3. Exercise 8 in section 4.1 on page 310 in the textbook.

4. Exercise 32 in section 4.1 on page 311 in the textbook.

5. Exercise 20 in section 4.3 on page 325 in the textbook.

#### Hand these exercices in before noon monday october 24th.

Also take a look at the following excercices:
From section 4.1:
7, 19, 33, 41.
From section 4.3:
11, 21, 33.

Remember that the above exercises are for you to practice on, and that you get the most out of them by trying to solve them yourselves (not by looking at someone else solving them!). The exercises in bold are more "interesting" than the others and it is more likely that they will be covered in the sections.

hh (hja) hi.is, October 17th, 2005.