Solution of problem N4831 probability theory

Solution of problem N4831 probability theory

4831. There are n=10 parts in a box, among which a=6 are painted. Two parts are taken out at random. Find the probability that:
1) both removed parts will be painted;
2) one part is painted and the other is unpainted (the order of appearance of parts is not taken into account);
3) at least one of the two parts will be painted.

Additional information:

Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)