The point $P(x,y,z)$ in three-dimensional co-ordinate system is said to have integral co-ordinates if  $x,y,z\in$ I. Now consider the following curves,  $C_1\equiv xyz=60$
$$\begin{gathered} P_1\equiv x+y+z=15 \\ {P}_2\equiv x+y+z=20 \end{gathered}$$
Let  $P_1$  cuts x, y & z axes at point A,B & C respectively and  $P_2$  cuts x, y& z axes in points P,Q&R respectively. Let ‘O’ be the origin.
$S_1=$set of points with positive integral co-ordinates lying on the curve $C_1.$ 
$S_2=$ set of points with integral co-ordinates lying inside the tetrahedron OABC.
$S_3=$ set of points with integral co-ordinates lying inside the tetrahedron OPQR.
On the basis of above information, answer the following questions: