Question

В двух классах 80 человек. Играют в баскетбол 52 человека, плаваньем 50, лыжи 54. 30 И баскетболом и плаваньем, 32 баскетболом и лыжами, 36 лыжами и плаваньем. 2 освобождены. Сколько людей занимаются всеми перечисленными видами спорта?

Answer 1

52+50=102
54+30=84
32+36=68
102+84+68=254
254-2=252

Answer 2

Problem Analysis

We are given the following information: - There are 80 people in two classes. - 52 people play basketball. - 50 people swim. - 54 people ski. - 30 people play both basketball and swim. - 32 people play basketball and ski. - 36 people ski and swim. - 2 people are not involved in any of the mentioned sports.

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

Solution

To solve this problem, we can use the principle of inclusion-exclusion. We will start by adding the number of people who play basketball, swim, and ski. Then, we will subtract the number of people who play both basketball and swim, the number of people who play basketball and ski, and the number of people who ski and swim. Finally, we will add back the number of people who play all three sports.

Let's calculate the number of people who play all three sports step by step:

1. Number of people who play basketball, swim, and ski: - 52 (basketball) + 50 (swim) + 54 (ski) = 156.

2. Number of people who play both basketball and swim: - 30.

3. Number of people who play basketball and ski: - 32.

4. Number of people who ski and swim: - 36.

5. Number of people who play all three sports: - Let's assume this number is x.

Now, we can use the principle of inclusion-exclusion to calculate the value of x:

- Number of people who play basketball, swim, and ski = Number of people who play basketball + Number of people who swim + Number of people who ski - Number of people who play both basketball and swim - Number of people who play basketball and ski - Number of people who ski and swim + Number of people who play all three sports. - 156 = 52 + 50 + 54 - 30 - 32 - 36 + x. - Simplifying the equation: 156 = 88 + x. - Solving for x: x = 156 - 88 = 68.

Therefore, 68 people participate in all three sports.

Answer

The number of people who participate in all three sports (basketball, swimming, and skiing) is 68.