Your home security system is disarmed when 3 different number buttons are pushed in a certain order. No button can be pushed twice! A robber attempts to break into your house.
What is the probability that he can disarm the device by randomly guessing 3 of the 10 buttons?
(buttons from 0-9)
there are 10P3 valid ways to pick the 3 buttons
only 1 will work, so
P(works) = 1 / 10P3
actually, if the robber does not know that a digit cannot be repeated, then
P(works) = 1/10^3