\documentclass[14pt]{extreport}
\usepackage[english]{babel}
\usepackage[utf8x]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage[makeroom]{cancel}
\usepackage{tabularx}
\usepackage{xcolor}
\usepackage{relsize}
\pagenumbering{gobble}
\title{Calculating the Probability for Winning a 649 Lottery}
\author{Adrian D'Costa}
\begin{document}
\maketitle
\section{Introduction}
This Article will demonstrate how to calculate the probability for winning a 649 lottery using Permutation and Combination.
\section{What is Probability?}
Probability is a number between 0-1 inclusively that projects or predicts the likelihood of an event occurring in this universe of ours. If the number is closer to 1 the event is more likely to take place.
\subsection{Computing the probability of winning 649 Lottery}
\begin{align*}\text{The probability of winning 649} &= \frac{\text{the total number of winning lottery ticket}}{\text{the total number of possible winning ticket}}\end{align*}
The total number of winning ticket = 1
\begin{align*}\text{The total number of possible winning ticket} &= \text{choosing 6 unique numbers out of 49} \\& \text{numbers without repetition}\end{align*}
\begin{align*}\text{The total number of possible winning ticket} =& \binom{49}{6}\\ =& \frac{49!}{6! (49 - 6)!}\\ =& \frac{49 \times 48 \times 47 \times 46 \times 45 \times 44 \times 43!}{(6 \times 5 \times 4 \times 3 \times 2 \times 1) \times 43!}\\ =& 13,983,816 \\ & \approx{14,000,000}\end{align*}
\begin{align*}\text{The probability of winning 649} & \approx{\frac{1}{14,000,000}}\end{align*}
According to Google.com Canada's population was 35.85 million in year 2015.
That is why I do not believe in luck. I strongly believe luck is hard work and what one makes out of his or her own life. I believe in Mathematics, Probability and Statistics. So I wish you a high probability in winning the lottery.
\end{document}
