Topic 7: Permutation and Combination

Permutation - The number of different ways that a certain number of objects can be arranged in order from a huge number of objects.

• An ordered list, order matters.
• Keyword(s) : Arrangement

Formula: 

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

• Un - ordered group/list
• Keyword(s) : choice, selection, election.

Formula : 

Example 1,

How many ways can you arrange these 4 objects.

Permutation :

N! / (N - n)!  = 4! / (4 - 4)! = 4 x 3 x 2 x 1 / (1)  = 24 ways

Combination :

N! / n!(N - n)! = 4! / 4!(4 - 4)! = 4 x 3 x 2 x 1 / 4 x 3 x 2 x 1 x 1 = 1 ways


Example 2,

How many ways can you arrange of 7 objects picking 5 at a time?

Permutation:

N! / (N - n)! = 7! / (7 - 5)! = 7 x 6 x 5 x 4 x 3 x 2 x 1 / 2 x 1 = 2520 ways

Combination:

N! / n!(N - n)! = 7 / 5!(7-5)! = 7 x 6 x 5 x 4 x 3 x 2 x 1 / 5 x 4 x 3 x 2 x 1 x 2 x 1 = 21 ways