\problemdata      
        {counting-9} % latex-friendly label for the prob.
        {Counting} % The topic(s) of the problem content.
        {Rosen Exercise 4.6-42} % Source (if known)
        {S02 CP8W; F01, TU9; S98 PS7} % Usage (list ones you are aware of).
        {Christos Kapoutsis, S02} % Last revision info (author, date).

\begin{problem}
A shelf holds 13 books in a row. How many ways are there to choose
five books so that no two adjacent books are chosen?

\solution{There are 5 bars (chosen books), and therefore there are 6
places where the 8 stars (non-chosen books) can fit (before the first
bar, between the first and second bars,..., after the fifth bar).
Each of the second through fifth of these slots must have at least one
star in it, so that adjacent books are not chosen. Once we have placed
these 4 stars, there are 4 stars left to be placed in 6 slots. The
number of ways to do this is therefore ${{6+4-1}\choose{4}}={9\choose
4}=126$.}
\end{problem}
