PERMUTATION AND COMBINATION

Permutation and Combination, which one is which?

Let's start with Permutation,

The number of different ways that a certain number of objects can be arranged in order 

from a large number of objects.

- Ordered lists (Order matters)

- Key Word : Arrangements

FORMULA

!    =   Factorial (number of ways)

N! =   Permutation

n   =   Number selected

     N !          

( N - n ) ! 

Example:


1! = 1                                                      = 1
2! = 2 x 1                                         = 2
3! = 3 x 2 x 1                                          = 6
4! = 4 x 3 x 2 x 1                             = 24
5! = 5 x 4 x 3 x 2 x 1                       = 120
6! = 6 x 5 x 4 x 3 x 2 x 1                 = 720
7! = 7 x 6 x 5 x 4 x  3 x 2 x 1          = 5,040   




Second, Combination

The number of different ways that a certain number of objects as a group can be selected
from a larger number of objects.

- Unordered group/ set : order does not matter
- Key Word : Choice, Selection, Election

FORMULA

!    =  Factorial (number of ways)
N! =  Combination
n   =  Number selected

        N !       
n ! ( N - n ) !