# Counting & Probability

### Bored of formulas? Do you want to ACTUALLY understand math?

## If you are here, you have to say goodbye to the good old days when counting was simply 1,2,3….

Basically the result is a number of two digits

What is the number of all possible outcomes?

Solution:

-Method 1: We apply the tree method that we all know since we were kids, but that would take too long!

-Best method: We can call it the Square Method:

**4**(it can be either 1,2,3,4)**x3**( has three because one was already used up)=**12 possibilities**

**Lets say we take the SAME experiment, but know the chocolates are put back in place****… because of guilt o:). **We apply the Square method

**4x4=16 Possibilities**

## Factorial?

1!=1

n!= n(n-1)(n-2)…..1

What is all of this?!

Example:

Tara,Basem,Hiba and Hadi have in english exam in turn.

Determine all possible turns for the four students.

**4!= 4x3x2x1=24**

**When it comes to words and letters:**

*Maths? 5! (having 5 letters)

*Lili, here we have repeated letters so saying 4! is considered wrong, so what we do is we divide the number of total letters in the word over the number of letters being repeated like this

(4!)/ (2!2!)

__Harder Example:__

__3 boys and 2 girls want to sit down on a bench.__

**1)How many different ways can they sit?**

5!——> 5x4x3x2x1=120 ways

**2) Same question, but this time boys are next to each other as well as boys**.

3!x2!x2=24