MDM4U – Grade 12 Data Management – Permutations Test

Grade 12 Data Management – Permutations

Multiplicative Principles

  • If one operation can be performed in K1 ways, and for each operation that can be performed K2 ways, and for each operation that can be performed K3 ways..
    • All of these ways can be performed K1 x K2 x K3.. ways

 

Additive Principles

  • If one mutually exclusive action can occur in K1 ways and a second can occur in K2 ways, then there are K1 + K2.. ways in which these actions can occur.

 

Methods

  • If a set of operations can be used to determine a result, then it’s called  Direct Method
  • However, if it is difficult to determine directly, an indirect method may be used by subtracting certain possibilities so they are eliminated

 

Factorial Notation

  • For the following: r < n
    • n! = n(n-1)(n-2)(n-3)(n-4)… (n-r+1)(n-r)!, n belongs to natural numbers
    • n!/(n-r)! = n(n-1)(n-2)(n-3)(n-4)… (n-r+1)(n-r)!/(n-r)!
    • ie. 6! = 6*5*4*3*2*1

 

Permutations with some elements alike

  • In general, the number of different arrangements of n objects K1 alike of one kind and k2 alike of another kind is:

n! / (k1!)(k2!)

  • ie. in the word “COOL”, the permutations are as follows:

4! / (2!)  = 12