Math Fundamentals18 sections · 814 units
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Overcounting and Correction

When simple rules fail

Sometimes the product rule counts some outcomes multiple times. When this happens, you need to correct for overcounting by dividing.

For example, if you want to count 2-person committees from 5 people, multiplying 5×4=205 \times 4 = 20 overcounts because picking Alice then Bob is the same committee as picking Bob then Alice.

Divide by 2!=22! = 2 to get the correct answer: 20/2=1020 / 2 = 10 committees. This pattern leads to combinations, which you will learn in a later section.