Solution of problem N3099 probability theory

Solution of problem N3099 probability theory

3099. In the box there are 5 blue, 4 red and 3 green pencils. 3 pencils are taken out at random. What is the probability that:
a) They are all the same color;
b) They are all different colors;
c) Among them are 2 blue and 1 green pencil.

Additional information:

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