Question

In a survey of 25 students, it was found that 15 had taken mathematics, 12 had taken physics and 11 had taken chemistry, 5 had taken mathematics and chemistry, 9 had taken mathematics and physics, 4 had taken physics and chemistry and 3 had taken all the three subjects.

Find the number of students that had taken only one of the subjects.

• A. 10
• B. 11
• C. 12
• D. 15

Answer 1

The correct option is B 11

Let $M=$ Set of student who taken Mathematics only

$C=$ Set of student who taken chemistry only.

$P=$ Set of student who taken Physics only.

$\therefore n\left(M\right)=15,n\left(P\right)=12,n\left(C\right)=11,n(M\cap C)=5,n(M\cap P)=9,n(P\cap C)=4,n(M\cap P\cap C)=3$

The number of students that had taken only one of the subjects

$n\left(onlyM\right)+n\left(onlyP\right)+n\left(onlyC\right)=4+2+5=11$.