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 exactly two of the three subjects.

• A. 9
• B. 10
• C. 11
• D. 12

Answer 1

The correct option is A 9

Total no. of student=25

Let n(M)=student who studying mathematics

n(C)=student who studying chemistry

n(P)=student who studying Physics

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

Number of student who studying mathematics and physic but not chemistry

$\Rightarrow n(M\cap P)-n(M\cap P\cap C)$

$\Rightarrow 9-3=6$

Number of student who studying chemistry and physic but not mathematics

$\Rightarrow n(P\cap C)-n(M\cap P\cap C)$

$\Rightarrow 4-3=1$

Number of student who studying mathematics and chemistry but not physics

$\Rightarrow n(M\cap C)-n(M\cap P\cap C)$

$\Rightarrow 5-3=2$

$\therefore$No.of student who had taken two of the three subjects$=6+1+2=9$