a)
The circles at the top represent a Venn diagram for the question, where the regions A to H have the following meanings:
A Students not enrolled for APD, AO or AS
B APD students
C AO students
D AS students
E APD and AS only
F AO and AS only
G APD and AO only
H APD, AO and AS students
A+B+C+D+E+F+G+H=960 (all students)
B+E+G=320 (APD total)
C+F+G=490 (AO total)
D+E+F=440 (AS total)
It is assumed that the three totals above do not include those taking all three subjects.
A=90 (other total)
E=140 (APD and AS)
F=170 (AS and AO)
G=150 (APD and AO)
H=80 (all 3)
Therefore B=320-290=30, C=170, D=130
b) APD only=B=30; AO only=C=170
c) 2 subjects only=E+F+G=460
d) not AS=960-(D+E+F+H)=960-520=440