The principle of inclusion and exclusion and its application
The principle of inclusion and exclusion is called the principle of elimination. It is a very common and very important counting principle in combinatorial mathematics, and is often used in fields such as probability theory and number theory.
(1) Basic way of thinking
Turn a difficult problem into a simple one, and get the solution of this difficult problem by summing up several simple problems, that is, to solve the problem that is not easy to solve by direct counting by indirect counting.
The core idea: the spirit of ants chewing bones! ! !
(2) Introduction to the principle of inclusion and exclusion
The principle of inclusion and exclusion is generally used to solve the following problems:
p1, p2….pm are the m properties involved in the elements in the set S, then what is the number of elements in the set that do not have properties p1, p2….pm?
(3) Application of the principle of inclusion and exclusion
3.1 Counts with repeating combinations
3.2 Dislocation arrangement
3.3 Arrangements with prohibited positions
(The deadline is April 9, 2018, and the next time you have time, continue to update)