Question: 48. We are given n (n > 5) points in space, no three of which lie on the same straight line. Let # be the

48. We are given n (n > 5) points in space, no three of which lie on the same straight line. Let # be the family of planes defined by any three of these points. Suppose that the points are situated in a way that no four of them are coplanar, and no two planes of # are parallel. From the set of the lines of the intersections of the planes of #, a line is selected at random. What is the probability that it passes through none of the n points? Hint: For i = 0, 1, 2, let Ai be the set of all lines of the intersections that are determined by planes having i of the given n points in common. If |Ai| denotes the number of elements of Ai, the answer is |A0|/ ! |A0|+|A1|+|A2| " .

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