Question

.In a group of 900 students, 612 like football and 540 like Volleyball./ Ifall the students like at least a game finda. How many students like both the game?b. How many students like only Football?​

Answer 1

In a group of 900 students, 252 students like both football and volleyball, and 360 students like only football. The principle of inclusion-exclusion is used to find these numbers by adding the students who like each game and subtracting those who like both to avoid double-counting.

Step-by-step explanation:

To solve this problem, we can apply the principle of inclusion-exclusion for two sets. First, we add the number of students who like football and volleyball, which gives us the total number of students who like at least one of the games; however, students who like both games are counted twice in this total. Therefore, we need to subtract the number of students who like both to avoid double-counting.

Let's calculate:

• Total number of students (n(U)) = 900
• Students who like football (n(F)) = 612
• Students who like volleyball (n(V)) = 540

Using the formula n(F ∩ V) = n(F) + n(V) - n(U) to find the number of students who like both, we get:

n(F ∩ V) = 612 + 540 - 900 = 252

Therefore, 252 students like both football and volleyball.

To find how many students like only football, we subtract the number of students who like both games from the total number who like football:

n(F - V) = n(F) - n(F ∩ V) = 612 - 252 = 360

Thus, 360 students like only football.