The answer is 30.
first consider how many distinct rods of x-M-y can be made (a-M-b and b-M-a are the same) .
No. of such ways = 6!((2!^3)*3!)=15
now consider a situation→ a-M-c; b-M-d; e-M-f are the three possible rods as shown in figure
align the rods with the x-y-z axis with M as origin in any order you want.
lets call M-c as the vector from M to point c hence we see that Ma= -Mc and as such it follows all vector properties . Also take |Mc|=1 just to keep it simple.
This is the tricky part now:
if you define a rule that (Mb X Me= Mc)→eq1; (X here is cross product) whenever you combine the above given rods ,then you can check for yourself that there is a unique octahedron( in fig above) and rotating about any of x, y or z axis wont make any change in relative positions of molecules . In fact if you fix the relative positioning of any three points(e ,b ,c lets say) then the octahedron becomes unique. You can also define (Mc X Md= -Mf )→eq2 ;but you’ll see that eq2 is just eq 1 written in another way( just take cross product with Md ).
But if we defined (Mb X Me = Ma) then the octahedron would have been different one in which a & c have switched places. In fact it would be the mirror image of the octahedron shown above. And as a result all the relative positions of any three molecules which are not on same rod will also change! All the cross products which were +ve become -ve now . Cross products are basically a rotation property. Hence there are enantiomeric pairs.
So we see we have two such rules for 3 given rods, hence total no. of such combinations possible = 15 *2= 30.
n×3=15...so value of n is 5