There are 8 books in a shelf that consist of 2 paperback books and 6 hardback books. If 4 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?  Choose the correct choice from the following answers.
A) 40  B) 45  C) 50  D) 55  E) 60
It's almost always better to solve "at least one" combinations/probability questions with {at least one}={total}-{none}.   Total # of selections of 4 books out of 8: C48=70C84=70;   Total # of selections of 4 hardback books out of 8 (so none paperback): C46=15C64=15;   {at least one}={total}-{none}=70-15= 
<gadget id="calculator">70-15</gadget>
<output>55</output>
55.   Answer: 55
<result>D</result>
There are 8 books in a shelf that consist of 2 paperback books and 6 hardback books. If 4 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?