Solution of problem N4830 probability theory

Solution of problem N4830 probability theory

4830. The box contains 16 parts, 10 of which 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)