Question

Из 27 учеников класса 15 занимаются спортом,а 18 музыкой. Некоторые из тех, которые занимаются и музыкой и спортом ходят в театральный кружок. Какое наибольшее число ученников могут посещатьтеатральный кружок?

Answer 1

18 человек потому что они меньше занимаются

Answer 2

Calculating the Maximum Number of Students in the Drama Club

To calculate the maximum number of students that could be in the drama club, we can use the principle of inclusion-exclusion.

Given: - Total number of students in the class: 27 - Number of students involved in sports: 15 - Number of students involved in music: 18 - Some students are involved in both music and sports - We want to find the maximum number of students that could be in the drama club

Let's calculate step by step.

1. Total Students: 27 2. Students involved in sports: 15 3. Students involved in music: 18 4. Students involved in both music and sports: Unknown

Calculating the Maximum Number of Students in the Drama Club

To calculate the maximum number of students that could be in the drama club, we can use the principle of inclusion-exclusion.

Given: - Total number of students in the class: 27 - Number of students involved in sports: 15 - Number of students involved in music: 18 - Some students are involved in both music and sports - We want to find the maximum number of students that could be in the drama club

Let's calculate step by step.

1. Total Students: 27 2. Students involved in sports: 15 3. Students involved in music: 18 4. Students involved in both music and sports: Unknown

To find the maximum number of students that could be in the drama club, we can use the principle of inclusion-exclusion. This principle states that for three sets A, B, and C:

\[ \left| A \cup B \cup C \right| = \left| A \right| + \left| B \right| + \left| C \right| - \left| A \cap B \right| - \left| A \cap C \right| - \left| B \cap C \right| + \left| A \cap B \cap C \right| \]

Where: - \( \left| A \right| \) represents the number of students involved in sports - \( \left| B \right| \) represents the number of students involved in music - \( \left| C \right| \) represents the number of students in the drama club - \( \left| A \cap B \right| \) represents the number of students involved in both music and sports

Given: - \( \left| A \right| = 15 \) - \( \left| B \right| = 18 \) - \( \left| A \cap B \right| \) is unknown

We want to find the maximum value of \( \left| C \right| \).

Using the principle of inclusion-exclusion, we can calculate the maximum number of students that could be in the drama club.