The faculty member in question has a hard time remembering the order of the words in his password, so he’s decided to ensure that the three words he chooses from this dictionary are different and...

The faculty member in question has a hard time remembering the order of the words in his password, so he’s decided to ensure that the three words he chooses from this dictionary are different and appear in alphabetical order in his password. (For example, the password ADOBESCUBAFOXES is forbidden because SCUBA is alphabetically after FOXES.)

 How many passwords fit this criterion? Solve this problem as follows. Let P denote the set of three-distinct-word passwords (the set from Exercise 9.64). Let A denote the set of three-distinctalphabetical-word passwords. Define a function f : P → A that sorts. Then use the Division Rule.

Exercise 9.64

How many passwords can be made by pasting together three distinct 5-letter words from this dictionary? (For example, the password ADOBESCUBAADOBE is forbidden because ADOBE is repeated.)