MEDAL FOR ANSWER AND EXPLANATION
You have checked out b books from the library, where b is a number greater than 5. You plan to read three of the books and return them at the end of the week. In how many ways can you pick the books you will read first, second, and third?

Question

MEDAL FOR ANSWER AND EXPLANATION 
You have checked out b books from the library, where b is a number greater than 5. You plan to read three of the books and return them at the end of the week. In how many ways can you pick the books you will read first, second, and third?

anonymous · Answer

I am assuming the following:
a) The books are picked one at a time.
b) there is no replacement. i.e. 

Total number of books  = b

a) Number of ways of choosing the first book out of b books is b
   because I can choose either the book in  slot 1, or slot 2 ... up to the book in slot b
      Remaining books = b-1.
b) Number of ways of choosing the second book  = b-1
    Because there are only b-1 slots holding b-1 books
    Remaining  books = b-2
c) Number of ways of choosing the third book is b-2



But the total number of ways of choosing the first 3 books is b*(b-1)*(b-2)