counting

The document is a lecture on counting and permutations given by A.B. Benedict Balbuena from the University of the Philippines. It defines permutations as ordered arrangements of elements from a set. It discusses how to calculate the number of permutations of an n-element set and the number of permutations when there are multiple objects of different types. It also covers combinations, defining them as unordered selections from a set, and provides the formula to calculate the number of combinations. Finally, it discusses the pigeonhole principle and generalized pigeonhole principle along with examples.