# Introduction to Counting and Probability

# How much do I want to read more? 8/10

I so much love this book. It's maths like I like it: simple concepts you are comfortable with, then build up upon this, and have some "haha" moments along the ride.

I wonder what I like so much about maths.

What's nice about this book is it contains lots and lots of exercice so that rules become second nature to your mind, The answers to the exercices are very good too.

# How to use this book

## Learn by solving problems

Lots and lots of problems. Try to solve problems that you don't know how to do.

www.artofproblemsolving.com with forum, online classes, resource…

Students should try to solve problems before the new material is presented.

# Chapter 1- Counting is arithmetic

## 1.1 - Introduction

Important: Don't memorize!

Don't see this book as a series of problems in which you learn "tricks". All counting problems call for appropriate use of addition, substraction, multiplication, and division.

### Problem 1.1

How many numbers are in the list

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18

### Problem 1.2

7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29

### Problem 1.3

Given two positive numbers b > a. Find a formula for how many numbers there are between a and b inclusive.

### Problem 1.4

How many multiple of 3 are between 62 and 215?

### Problem 1.5

- How many multiple of 10 between 9 and 101?
- How many multiple of 10 between 11 and 103?
- Given (103-110) = (101-9) why the answer is different?

### Problem 1.6

How many 4-digit numbers are perfect cubes?

If people do not believe that mathematics is simple, it is only because they do not realize how ocmplicated life is

-- John Von Neuman

Numbers between 7 and 29 are numbers between (7-6) and (29-6): that is, between 1 and 23.

Numbers between a and b are numbers between a-(a+1) and b-(a+1).

Concept: When presented with a complicated problem, try to reduce or simplify it to a simpler problem that you know how to solve.

62 = 3x21 + something

215 = 3x71 + something

The list is 63, 64, …, 213

Or: 21, 22, …, 71

Or: 1, 2, … 51

Our list is 10, 11, … 21