Ready for PIE?
The ability to apply the principle of inclusion and exclusion allows us to solve more difficult problems in combinatorics. By finding the value to each part of the elements that have been double counted at each step, we can add or subtract down the line to ensure that each element in question has only been counted once.
Here are some ways to use PIE, give it a try!
- How many ways are there to arrange the letters of MASTERPIECE that avoid the word PIE?
- How many numbers between 1 and 1000 are not divisible by 2, 3, or 5?