When randomizing the order of Lord Of The Keys, the number of possible unique permutations in which we can obtain keys is given by:

However, there is one restriction: Shopkeeper's Key must be obtained before Elegant Key. This condition reduces the total number of valid permutations.

Without restrictions, the total number of permutations would be:

With the restriction, only half of these permutations are valid, therefore, the total number of valid permutations is: