Variation

Introduction

In the previous articles, we explored permutations as well as combinations with and without repetition, we will now explore variation!

Where do we use variation ?

Permutations are used when you have equal number of elements and positions unlike variations which is used when you have more elements than positions. Let's take an example to understand.

Variation with repetition

Photo by Towfiqu barbhuiya on Unsplash

We found a suitcase that contains 1 million $ we need to crack the code to open it! but you have only 3 chances to do it!

The code consists of numbers between 0 and 9 for only 3 positions!

How many variations ?

Variation with repetition formula :

"n" is the number of elements and "p" is the number of positions.

Solution :

• 10V3 = 10^3
• 10V3 = 1000

Variation without repetition formula

Now let's take the same example but without repetition !

"n" is the number of elements and "p" is the number of positions.

• 10V3 = 10!/(10-3)!
• 10V3 = 10!/7!
• 10V3 = 10*9*8*7!/7!
• 10V3 = 10*9*8
• 10V3 = 720