Editorial for LCC '23 Contest 1 J1 - Choosing a Costume

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Author: AZron

To find the total number of distinct costumes, you need to consider all possible combinations of choices, and to do this, you multiply the number of choices for each category. This is because of the fundamental counting principle, which states that when you have multiple independent choices to make, you can determine the total number of outcomes by multiplying the number of choices for each individual decision.

In this case, Shane has four independent choices to make when creating his costume: choosing a hat, choosing a shirt, choosing pants, and choosing shoes. Each of these choices has its own set of options.

When he selects a hat, there are 'A' choices available. When he selects a shirt, there are 'B' choices available. When he selects pants, there are 'C' choices available. When he selects shoes, there are 'D' choices available.

So, the multiplication is used to systematically combine all the individual choices to calculate the total number of distinct costumes he can create.