The lowest common denominator for 8 and 12 is 24. So you would need 3 packages of hotdogs and 2 packages of buns.
In the
plane, we have
everywhere. So in the equation of the sphere, we have

which is a circle centered at (2, -10, 0) of radius 4.
In the
plane, we have
, which gives

But any squared real quantity is positive, so there is no intersection between the sphere and this plane.
In the
plane,
, so

which is a circle centered at (0, -10, 3) of radius
.
7,8,6,5,9,10,20
Total:7
Even number:8,6,10,20
First pick:
4/7
Second pick:
3/6 or 1/2. As a result, the final answer is 2/7. Hope it help!