Question

Пожалуйста помогите решить!!!В классе 40 учеников. Из них 26 занимаются баскетболом, 25 плаванием, а 27 - лыжным спортом, 15 - баскетболом и плаванием, 16- баскетболом и лыжами, 18- плавание и лыжи. 1 человек освобожден от физкультуры. Сколько человек занимаются всеми видами спорта?

Answer 1

15+16+18+1-40=10(ч.)

Answer 2

Problem Analysis

We are given the following information: - There are 40 students in the class. - 26 students play basketball. - 25 students swim. - 27 students participate in skiing. - 15 students play basketball and swim. - 16 students play basketball and ski. - 18 students swim and ski. - 1 student is exempt from physical education.

We need to determine the number of students who participate in all three sports.

Solution

To find the number of students who participate in all three sports, we can use the principle of inclusion-exclusion.

Let's denote: - A as the set of students who play basketball, - B as the set of students who swim, and - C as the set of students who ski.

We are given the following information: - |A| = 26 (the number of students who play basketball), - |B| = 25 (the number of students who swim), - |C| = 27 (the number of students who ski), - |A ∩ B| = 15 (the number of students who play basketball and swim), - |A ∩ C| = 16 (the number of students who play basketball and ski), - |B ∩ C| = 18 (the number of students who swim and ski), and - |A ∩ B ∩ C| = ? (the number of students who participate in all three sports).

We can use the formula for the principle of inclusion-exclusion to find |A ∩ B ∩ C|: |A ∩ B ∩ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

Substituting the given values: |A ∩ B ∩ C| = 26 + 25 + 27 - 15 - 16 - 18 + |A ∩ B ∩ C|

Simplifying the equation: |A ∩ B ∩ C| = 25

Therefore, there are 25 students who participate in all three sports.

Answer

There are 25 students who participate in all three sports.