Probability to open a door using all the keys I have 1 door and 10 keys. What is the probablity to open the door trying all the keys? I will discard every single key time to time.

Solution 1:
Hint: How many permutations are there for the order of the 10 keys?
Hint: How many permutations are there, where the last key is the correct key?

Solution 2:
Hint: The probability that the last key is the correct key, is the same as the probability that the nth key is the correct key. Hence ...
