Complementary counting
Complementary counting is counting the complement of the set we want to count, and subtracting that from the total number of possibilities, or the universal set for that particular problem. In problems that involve complex or overly complicated and tedious casework, complementary counting is often a far easier and more efficient approach. Within a problem statement, a large hint that complementary counting may lead to a quick solution is the phrase "at least".
Video
This is a video explaining the basics of casework, complementary counting, and overcounting (PIE): https://youtu.be/Zhsb5lv6jCI
