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?
To get at least one paperback book:
Either two paperback books and four hadrback books: 2C2 · 6C4 = 15
Or one paperback book and five hardback books: 2C1 · 6C5 = 12
Since these are mutually exclusive, adding them together = 27 ways.