Question

How do we solve this question

In a class of 31 students, 16 play football, 12 play table tennis and 5 play both games
(1) find the number of student who play
(i) at least one of the games
(ii) none of the games

Answer 1

Explanation:

Using the inclusion-exclusion principle, we can find the number of students who play at least one of the games as follows:

Number of students who play at least one of the games = number of students who play football + number of students who play table tennis - number of students who play both games

= 16 + 12 - 5

= 23

Therefore, 23 students play at least one of the games.

To find the number of students who play none of the games, we can subtract the number of students who play at least one of the games from the total number of students:

Number of students who play none of the games = total number of students - number of students who play at least one of the games

= 31 - 23

= 8

Therefore, 8 students play none of the games.