In a class of 40 students, 25 study Mathematics and 18 study Physics. If 3 students study … — JAMB UTME

In a class of $40$ students, $25$ study Mathematics and $18$ study Physics. If $3$ students study neither of the two subjects, how many students study both Mathematics and Physics?

Answer: 6 students

Answer

6 students study both Mathematics and Physics.

Subtracting the

3

students who study neither subject from the class total of

40

leaves

37

students studying at least one subject. Adding those studying Mathematics (

25

) and Physics (

18

) totals

43

. The excess of

43

over

37

represents the

6

students who study both subjects.

Step-by-Step Solution

Subtract the number of students studying neither subject from the total number of students in the class.

n(M \cup P) = 40 - 3 = 37

This gives the number of students who belong to at least one of the two sets.

Set up the inclusion-exclusion formula

n(M \cup P) = n(M) + n(P) - n(M \cap P)

37 = 25 + 18 - n(M \cap P)

Summing

n(M)

and

n(P)

double-counts the students who study both subjects.

Solve for the intersection

n(M \cap P)

n(M \cap P) = 43 - 37 = 6

Subtracting the union from the sum of the individual sets isolates the intersection value.

Key Concept

Principle of Inclusion-Exclusion for Two Sets

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