Question

In a group of EXPLORE students, 38 enjoy video games, 12 enjoy going to the movies and 24 enjoy solving mathematical problems. Of these, 8 students like all three activities, while 30 like only one of them.
How many students like only two of the three activities?​

Answer 1

Answer

The number of students that like only two of the activities are 34

Step-by-step explanation:

Number of students that enjoy video games, A = 38

Number of students that enjoy going to the movies, B = 12

Number of students that enjoy solving mathematical problems, C = 24

A∩B∩C = 8

Here we have;

n (A∪B∪C) = n (A) + n (B) + n (C) - n (A∩B) - n (B∩C) - n (A∩C) + n (A∩B∩C)

= 38 + 12 + 24 - n (A∩B) - n (B∩C) - n (A∩C) + 8

Also the number of student that like only one activity is found from the following equation;

n (A) - n (A∩B) - n (A∩C) + n (A∩B∩C) + n (B) - n (A∩B) - n (B∩C) + n (A∩B∩C) + n (C) - n (C∩B) - n (A∩C) + n (A∩B∩C) = 30

n (A) + n (B) + n (C) - 2·n (A∩B) - 2·n (A∩C) - 2·n (B∩C) + 3·n (A∩B∩C) = 30

38 + 12 + 24 - 2·n (A∩B) - 2·n (A∩C) - 2·n (B∩C) + 24 = 30

- 2·n (A∩B) - 2·n (A∩C) - 2·n (B∩C) = - 68

n (A∩B) + n (B∩C) + n (A∩C) = 34

Therefore, the number of students that like only two of the activities = 34.

Answer 2

Answer:

36 only

because the 2 student their not enjoying Thier outing