I am reading solution for this problem in Dimitri P. Bertsekas's book and I see this question post in this forum as well.
"suppose You rented a house and realtor gave you 5 keys, one for each of the 5 doors of house. unfortunately all keys look identical. so to open the front door, you try them at random.
=> Find the PMF (probability mass function) of the number of trials you will need to open the door, under the following supposition :
i. after an unsuccessful trial, you mark the corresponding key, so you never try it again
ii. at each level you are equally likely to choose any key"
However, I have hard time understanding the alternative solution on part ii.
The alternative solution for part ii in this book begins by saying: "Consider now an alternative line of reasoning to derive the PMF of X. If we view the problem as ordering the keys in advance and then trying them in succession, the probability that the number of trials required is x is the probability that the first x − 1 keys do not contain either of the two correct keys and the xth key is one of the correct keys...."
My question is: "Isn't there is only one correct key for each of the five doors? Why "two correct keys" are mentioned here? Can anyone help me to understand the beginning of the reasoning of this alternative answer?