MATHEMATICS

JAMB 2012 - Question 10

Mathematics 2012 JAMB Past Questions - Question 10: In a class of 46 students ,22 plays football and 26 play volleyball .if 3 students play both games how many play neither ?

In a class of 46 students ,22 plays football and 26 play volleyball .if 3 students play both games how many play neither ?
A:
B:
C:
D:
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Correct Answer

A

Explanation

3+19+23+x = 4622+23 =x = 4645 +x = 46x = 46-45x = 1To find the number of students who play neither football nor volleyball, we can use the principle of inclusion-exclusion.Let's denote:A = Number of students who play footballB = Number of students who play volleyballC = Number of students who play both football and volleyballAccording to the principle of inclusion-exclusion, the total number of students who play either football or volleyball is given by:A ∪ B = A + B - CGiven that A = 22, B = 26, and C = 3, we can substitute these values into the equation:A ∪ B = 22 + 26 - 3A ∪ B = 45Now, to find the number of students who play neither football nor volleyball, we subtract the number of students who play either football or volleyball from the total number of students in the class:Total students - (A ∪ B) = 46 - 45Total students - (A ∪ B) = 1Therefore, there is 1 student who plays neither football nor volleyball in the class of 46 students.