## Ballot numbers

In this post I want to present the ballot numbers, what are they? well, as you may alredy guessed, they are related to elections somehow. How exactly? that’s what we’re going to find out. Let’s start with a quick warm-up: Warming up “In an election with two candidates, thousand people participate. What is the probabilityContinue reading “Ballot numbers”

## The binomial coefficients

In the last post, we’ve finished talking about combinations and I mentioned there that the binomial coefficient are really important, so in this post I am going to focus on them and show some great properties of them. This post is also going to be the first one that I use combinatorical proofs, they willContinue reading “The binomial coefficients”

## Combinations

In the last post I’ve talked about permutations. In this post I am going to keep doing what I’ve started there – by introducing the the term of combinations: What are Combinations? A Combination of out of objects is a selection, where order doesn’t matter. Same as permutation, there are two types of combinations: combinationContinue reading “Combinations”

## Permutations

Let me ask you a question: “Suppose that I have a bag with 3 balls in it. How many ways are there to pick 2 balls out of it?” Well, what do you think? Most people would say that you have three ways of doing so, you can name the balls (first, second, third) andContinue reading “Permutations”

## Pigeonhole principle

Imagine that you are a pigeon owner, and let’s say that you have 10 pigeons. however, there is a problem – you have 9 pigenholes. How can you fit all the pigeons to different pigenholes? That’s right – you cant! You don’t have to be a mathematician in order to understand the situation. It isContinue reading “Pigeonhole principle”

## Combinatorics – Introduction

Hey! Welcome to the first combinatorics posts. What is combinatorics? It is actually a very wide subject, that appears everywhere in math. Basic Combinatorics can answer questions such as: If 1,000 people choose between two thing, in a random way, what is the chance that 500 chose the first thing, and the other 500 choseContinue reading “Combinatorics – Introduction”