Basic formula of inclusion and exclusion principle:
Question 1
There are 50 children in one group. They all like to eat one or two kinds of peppers or mustard. There are 36 people who like peppers and 20 people who like mustard. So, how many people like both?
explain
According to the basic formula of the principle of inclusion and exclusion, it can be concluded that both people like to eat =36+20-50=6 (people)
The principle of inclusion and exclusion involves three objects:
By extension:
Question 2
Mother spread three rectangular tablecloths on a rectangular table, overlapping each other, just covering the table completely. It is known that the areas of three tablecloths are 40 square decimeters, 36 square decimeters and 27 square decimeters respectively, in which the overlapping part of the first tablecloth and the second tablecloth is 5 square decimeters, the overlapping part of the second tablecloth and the third tablecloth is 7 square decimeters, and the overlapping part of the first tablecloth and the third tablecloth is 4 square decimeters. If the three overlapping parts are equal to 2 square decimeters, what is the area of this table?
analyse
Using this formula, we can get:
Namely:
abstract
Comparing 1 and 1 and 2 questions, we can easily find that the principle of inclusion and exclusion has a wide range of applications. Whether it is an arithmetic problem or a geometry problem, as long as the problem is set according to the meaning of each part in the formula of inclusion and exclusion principle, the inclusion and exclusion principle can be used to solve the problem.
2. You can also try to solve the problem with Wayne's drawings. In fact, the graphic method is exactly the same as the formula method. The former is more vivid and the latter is faster. You should use two methods flexibly when doing the problem.
homework
1. A school 120 80 boys and 80 girls, a language contest 120 girls and 80 boys. It is understood that there are 260 students in this school, of whom 75 boys have participated in these two subjects. How many girls took only one subject?
There are 48 students in one class, among whom 27 can swim, 33 can ride a bike and 40 can play table tennis. So, how many students in this class can play at least these three sports?
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