What is the principle of exclusion and the principle of pigeon coop?

Principle of inclusion and exclusion: first calculate the number of all objects contained in a content, regardless of overlapping parts, and then exclude the number of repeated calculations, so that the calculation results are neither omitted nor repeated. This counting method is called inclusion and exclusion principle.

Pigeon cage principle: There are ten apples on the table. If we put these ten apples in nine drawers, no matter how we put them, we will find at least two apples in one drawer. This phenomenon is what we call the "pigeon hole principle". The pigeon hole principle roughly means: "If each drawer represents a collection, then each apple can represent an element. If there are n+ 1 elements in n sets, there must be at least two elements in a set. " The pigeon coop principle is sometimes called the pigeon coop principle. This is an important principle in combinatorial mathematics.

Extended data:

Construction method of drawer

The core of applying pigeon coop principle is to analyze clearly which is the object and which is the drawer. For example, there are 12 zodiac signs, so at least one of any 37 people has at least four zodiac signs. At this time, the zodiac is regarded as a 12 drawer, so a drawer has 37/ 12, that is, the remainder of 3 is 1, and the integer is considered upward, so here it is 3+ 1=4 people, but here it should be noted that the remainder in front is 1, and what is added here is

So in the problem, one more object and one less drawer. For example, the above question belongs to 12, which is the corresponding drawer, and 37 people are the corresponding objects, because 37 is greater than 12.

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