There's no need for a complicated solution here. We're selecting 3 people from 8 and we want to know the probability Don is selected. That's just like lining the 8 people up, and asking the probability Don is one of the first 3 people in line. There are 8 spots for Don, 3 of which are among the first three spots, so the probability must be 3/8.
edit - Or to look at it a different way, each of the 8 people is as likely as anyone else to be selected for A, for B, or for C. That is, the probability Don is selected for A is 1/8, for B is also 1/8 and for C is 1/8, so the probability he is selected for one of the three is 1/8 + 1/8 + 1/8 = 3/8.
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