Discrete Mathematics
# Principle of Inclusion and Exclusion

But wait, hold on. Some of those multiples of 5 are odd, so they have been counted twice! This is where the Principle of Inclusion and Exclusion kicks in and saves us from making a mistake. By removing the 10 numbers that are both odd and multiples of 5, we find that there are actually 60 such numbers, not 70. If you want to tackle all sorts of counting problems, be sure to *include* this tool in your repertoire and *exclude* mistakes from your math.

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