Combinatorics

Lecture 5 of ENSC 180

Basics

• Tables

  • to make a table
    • T=table(x,y,z);
      • you must define the variables (matrix/list)
  • Dot Indexing

The addition Principle

• (AP) or rule of sum

  • let say we have events A and B, they are independent

    • example: we can choose either to watch a movie with 3 options for that movie or we can go eat food with 4 options for the food place
      • so the total number of options is just $|A|\cup |B|=|A|+|B|$

  • so we can say that

    • ${\bigcup }_{i=1}^k{A}_i={\sum }_{i=1}^k|A_i|$

The Multiplication Principle

• (MP)

  • lets say we have events A and B, and they are consecutive

    • example: we can watch a movie A (3 options) and go out to eat B (4 options)
      • so the total number of possibilities are $A\ast B$

  • We can write this as

    • ${\prod }_{i=1}^r{n}_i$

Permutations

• Different orders

  • K orders, N events

    • $P_K^N$

  • How to use permutations in matlab

    • Anonymous Function is used a lot here
    • P=@(n,k)factorial(n)/factorial(n-k);
      • then we can input values of n,k
        • this code is BAD it over flows and doesn’t give outputs because of the nature of factorials
    • P=@(n,k)prod([n-k+1:n]);
      • im going to be honest i have no idea how this works

  • Built in permutation function

    • x=[a,b,c]
      • >>perms(x)
    • randperm
      • gives vector counting until n randomly