Counting

Counting

1. Introduction

   • Permutations (n!)
   • no of choices ^ no of rounds

2. Selection

   • Case 1: Order matters and repetitions allowed
   • Case 2: Order matters and no repetitions
     • P(n,r) or nPr = n(n-1)(n-2)...(n-r+1) = n! / (n-r)!
   • Case 3: Order does not matter and no repetitions
     • Example: In how many ways can 5 students form a committee from 15?
       • Assume order matters: nPr =360360
         • Order doesn't matter: each set of 5 students are counted 5! = 120
           • 360360 / 120 = 3003
   • Case 4: Order does not matter and repetitions allowed
     • Example:Given 4 types of candy, how many ways can you get 7 pieces?
       • Method 1
       • Method 2

3. Theorem: r-combination: C(n,r) or nCr

   • = P(n,r) / r! = n! / r!(n-r)!