Lesson 58 - Permutations Involving different objects

Investigate:
Two letters, A and B, can be written in two different orders, AB and BA, These are permutations or A and B.
a) List all of the permutations of 3 letters A, B , and C.
ABC, ACB, BAC, BCA, CAB, CBA
 3  x 2 x 1 = 6
How many permutations are there?
    6

b) List all of the permutations of 4 letters A, B, C, and D
ABCD, ABDC, ACBD, ACDB, ADBC, ADCB
BCAD, BCDA, BADC, BACD, BDAC, BDCA
  How many permutations are there?
  4 x 3 x 2 x 1= 24

c) Predict the number of permutations of 5 letters A, B, C, D, and E
  5 x 4 x 3 x 2 x 1 = 5!
! : 5 4 3 2 1

Example 1:
When you press the "scramble" button on a cd player it plays a permutation of the songs on the CD. If the cd has 5 songs on it, how many permutations of the songs possible?

5! or 5p5 = 120                5p5: 5 songs ,  p: means how many your picking, you are picking 5


Factorial Notation:
1! = 1
2!= 2 x 1
3!= 3 x 2 x 1
n!= n (n-1)(n-2)(n-3) ......1

An ordered arrangement of distinct objects is called a permutation
The number of permutations of n distinct objects is n!
The number of permutations of n distinct objects taken r at a time is npr

Example 2:
np2= n!/ (n-2)!    
n(n-1)(n-2)!/ (n-2)!
= n(n-1)