Combinatorics … Whaaaa

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Its a fancy formula

An example: Lets create 125 unique NFTs.

If you have 5 different heads, 5 different sets of eyes, and 5 different hats, the total number of unique combinations would be: 5 × 5 × 5 = 125

So, you can make 125 unique images!

The formula is based on combinatorics. When you have multiple sets of items (like heads, eyes, and hats) and each item can pair with any other from the other sets, the total number of unique combinations is calculated by multiplying the number of options in each set.

In general, if you have:

  • n1​ options for the first set (e.g., heads),
  • n2​ options for the second set (e.g., eyes),
  • n3​ options for the third set (e.g., hats),

The total number of unique combinations is: n1 × n2 × n3 ​

For your example: 5 × 5 × 5 =125

If you add more sets (like eyeglasses, mouths, etc.), you just keep multiplying the number of options for each new set.

This method is called the rule of product (or multiplication principle), which is a core concept in combinatorics. It’s used when you need to calculate the total number of outcomes where multiple independent choices or events are involved.

In more advanced combinatorics, you can deal with problems involving permutations (where the order matters) and combinations (where the order doesn’t matter), factorials, and more.

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