Question

In one class 18 students play basketball, 14 students play soccer and 10 students play volleyball. 5 students play soccer and volleyball, 7 students play basketball and volleyball and 10 students play basketball and soccer. 4 students play all three sports. How many students are there in the class if every student plays at least one sport.​

Answer 1

Question:-

In one class 18 students play basketball, 14 students play soccer and 10 students play volleyball. 5 students play soccer and volleyball, 7 students play basketball and volleyball and 10 students play basketball and soccer. 4 students play all three sports. How many students are there in the class if every student plays at least one sport.

Required Answer:-

Given:-

• 18 students play basketball
• 14 students play soccer.
• 10 students play volleyball
• 5 students play soccer and volleyball
• 7 students play basketball and volleyball
• 10 students play basketball and soccer
• 4 students play all three sports

To Find:-

• Number of the students in the class.

Solution:-

○ Kindly see the attachment

Now let,

Number of students who play basketball = n(B) = 18

Number of students who play soccer = n(S) = 14

Number of students who play volleyball = n(V) = 10

Now,

Number of students who play basketball and soccer n(B ∩ S) = 10

Number of students who play soccer and volleyball n(S ∩ V) = 5

Number of students who play basketball and volleyball n(B ∩ V) = 7

Number of students who play all three sports n(B∩ S ∩ V) = 4

Therefore,

Number of students in the class = n(B U S U V)

Now, we know that:-

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

According to the question,

n(B U S U V) = n(B) + n(S) + n(V) - n(B ∩ S) - n(S ∩ V) - n(B ∩ V) + n(B ∩ S ∩ V)

Substituting the values:-

= 18+14+10-10-5-7+4= 24

Hence, there are 24 students in the class