In a class of 55 students the number of students studying subjects are , 23 iin Mathematics 24.in physics 19in chemisty 12 in Mathematics and physics ,9 in Mathematics and chemistry ,7 in physics and chemistry and 4 in all the three subjects.
the number of students who have taken ecactly one subject is

Options

A. 6
B. 9
C. 7
D. none of these

Answer

D

Explanation

Let M,P and be the sets of students studying mathematics ,physics and chemistry repectively . We have ,
`m(M) = 23,n (P) =24,n(C) =19 ,n (M cap P) =-12,`
`n(M cap C)=9,n(PcapC)=9,n(PcapC)=4`
`therefore ` Number of students studying exactly one subject
`=n(M) +n(P) +n( C) -2{n(M cap P)+n(PcapC) + n(McapC)}+3n(Mcap Pcap C)`
`=23+24+19-2{12+9+7}+3xx4`
`=66-2xx28+12=22`