a) The first calculation is simply picking 3 winners out of 8=8C3=56. There are 6 ways of arranging the winners in order of gold, silver, bronze, so 56*6=336.
b) Out of the 6 ways of arranging G, S, B (gold, silver, bronze) two of them are GSB, GBS for the 3 winners. So the probability that one particular athlete of the 8 athletes will obtain gold is 1/(56*3)=1/168.