Diluted inclusion–exclusion principle

Okay buddy, so you know how sometimes we have a lot of things to count but we also want to exclude some of them? Let's say we have a bunch of toys and we want to know how many animals toys we have, but we also want to exclude the toys that are not animals, like the cars or the puzzles.

So what we can do is use the diluted inclusion-exclusion principle, which is like a special way of counting things. It helps us count the total number of animals toys we have while making sure we do not count any cars or puzzles.

First, we count all the animal toys we have, so we have an idea of how many we have in total. Then we count all the non-animal toys we have, like the cars and the puzzles, but we want to exclude them from our final count.

Here comes the trick: we only count the toys that are both animals and non-animals. That might sound silly, but it actually helps us make sure we don't count the non-animal toys twice.

After that, we subtract the number of toys that are both animals and non-animals from the total number of animal toys we counted earlier. This gives us the final count of animals toys, without counting the non-animal toys like the cars or the puzzles.

So, in short, the diluted inclusion-exclusion principle is a way of counting things while making sure we exclude certain items from our count by subtracting their overlapping part. It might sound complicated, but it's just a clever way of counting things!