Question

There are 8 books on a shelf, of which 2 are paperbacks and 6 are hardbacks. how many possible selections of 4 books from this shelf include at least one paperback?

Answer 1

$\displaystyle \binom{6}{3}\cdot2+\binom{6}{2}=\dfrac{6!}{3!3!}\cdot2+\dfrac{6!}{2!4!}=\dfrac{4\cdot5\cdot6}{2\cdot3}\cdot2+\dfrac{5\cdot6}{2}=40+15=55$