Pr(3) = p(x=3)
You have the right idea, but something is going whacky.
In part a, you have a 1! in the denominator where there should be a 17! Even so, what you have written comes nowhere near 0.24. Must be more arithmetic errors going on. [(20*19*18)/(3*2)]*(0.05^3)*(0.95^17) = 0.0596 or so.
In part b, that probability is WAY to big. I'm thinking maybe you made the same kind of denominator error.
20*(.05^19)*0.95 + 0.05^20 is a very small number.
Good call on Part c.