# Counting and Probability

## Introduction

Everyday you count whether you are seeing how much money you have or how many subjects you have in a particular day … Also everyday you hear words like probably, more likely, less likely, chance. These are all related to probability.

Probability is when we are not sure something will happen. It is the comparison between the number of times an event could occur and the total number of possible events. While counting is naming or listing the units of a group or collection one by one in order to determine a total. ## What is n!? What are the basic principles of counting?What are permutations?

1) n factorial (n!) is defined as the product of all the integers from 1 to n.

n! = (n)(n − 1)(n − 2)...(3)(2)(1)

ex: 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

2) Basic Principles of Counting:

-Addition Rule: E = "day of the week"

n(E)= "number of outcomes of event E"

Let E1 and E2 be mutually exclusive (there are no common outcomes) events.

The number of times event E will occur is: n(E) = n(E1) + n(E2)

- Multiplication Rule:

Let E1 and E2 be two independent (one does not affect the other's outcome) events.

There will be n(E1) × n(E2) possible outcomes of the two events. n(E) = n(E1) × n(E2)

3) Permutations:

A permutation is an arrangement (or ordering) of a set of objects. There are 4

theorems:

-Theorem 1 - Arranging n Objects

-Theorem 2 - Number of Permutations

-Theorem 3 - Permutations of Different Kinds of Objects

-Theorem 4 - Arranging Objects in a Circle

For more detailed information, please visit http://www.intmath.com/counting-probability/counting-probability-intro.php