student going to form three choosing amung three subjects

Question

students going to a form three class are allowed to choose one or two of the subjects physic ,music and geography . none of them is allowed to take all the three subjects 24 students did not take any of the 3 subjects given that 6 students took only physics , 8 took only geography and 4 took only music , 7 students took 2 of the 3 subjects . a total of 14 students took geography and 9 took music find the total number of students who took physics and the total number of students in form 3

Answer 1

The Venn diagram above shows eight regions defined below:

A Physics only

B Music only

C Geography only

D Physics and geography but not music

E Music and geography but not physics

F Physics and music but not geography

G All three subjects

H None of the subjects

G=0, H=24 (no students took all 3 subjects, and 24 took none of the subjects).

A=6, C=8, B=4 (only one subject).

D+E+F=7 (two subjects).

C+D+E=14 (geography total), D+E=6 and F=1.

B+E+F=9 (music total), so E=9-4-1=4 and D=6-4=2.

Total physics=A+D+F=6+2+1=9.

Total students=A+B+C+D+E+F+G+H=6+4+8+7+0+24=49.