44. Given 5 points, no three of which lie on the same line. Find the probability that, by randomly selecting two points, a student will get the required line.
Solution. Let event $A$ be the selection of the desired line. The number of all possible outcomes is equal to the number of lines passing through the given five points. Since a line is determined by a pair of points and the order of the points within this pair does not matter, each pair must differ by at least one point. Therefore, we need to find the number of combinations of five elements taken two at a time, i.e.

$$
n=C_{5}^{2}=\frac{5!}{(5-2)!2!}=\frac{5!}{3!2!}=10
$$

Thus, the number of all possible pairs of points is 10, and only one pair of points is the desired one; therefore, $P(A)=1 / 10$.