Exactly one.
Infinitely many planes contain any two given points- it takes three (non-collinear) points to determine a plane.
Only one plane can contain three specific points.
Exactly one.
Three non-co-linear points are sufficient to uniquely define a single plane.
Exactly one.
Infinitely many planes may contain the same three collinear points if the planes all intersect at the same line.
Infinitely many planes contain any two given points- it takes three (non-collinear) points to determine a plane.
One.
Only one plane can contain three specific points.
There will always be a single plane through all three points.
Exactly one.
Yes, and in fact it is very likely that two planes will contain exactly one identical line. There are three possibilities:The planes are parallel, but not identical, in which case they contain no identical lines.The planes are not parallel, in which case they contain exactly one identical line.The planes are identical, and contain an infinite number of coplanar lines.
Three non-co-linear points are sufficient to uniquely define a single plane.
3 non-collinear points define one plane.
If the points are collinear, that means there's only one straight line. An infinite number of different planes can be drawn that contain one straight line.
There are no planes containing any number of given points. Two points not the same define a line. Three points not in a line define a plane. For four or more points to lie in the same plane, three can be arbitrary but not on the same line, but the fourth (and so on) points must lie in that same plane.