The probability none comes from C. is (30/80)*(29/79)*(28/78)=0.0494.
The three buttons have to be pressed in a certain order. Because three buttons have all been pressed many times, then the buttons will be assumed to be distinct.
The chances are then 3! or 6, and the probability is (1/6)
ABC
ACB
BCA
BAC
CAB
CBA
In this instance, there are 10 ways to choose each button, three times, independent, since the buttons don't have to be distinct. This is 10^3 or 1000, and the probability is (1/1000).
