Question

Find the number of students that had taken at least one of the three subjects

• A. 20
• B. 22
• C. 23
• D. 25

Answer 1

Answer: (C)

23

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 at least one of the three subjects

$\Rightarrow n(M\cup P\cup C)$

$\Rightarrow n\left(M\right)+n\left(P\right)+n\left(C\right)-n(M\cap P)-n(P\cap C)-n(M\cap C)+n(M\cap P\cap C)$

$\Rightarrow 15+12+11-9-4-5+3=23$