\problemdata      
        {counting-16} % latex-friendly label for the prob.
        {Counting} % The topic(s) of the problem content.
        {?} % Source (if known)
        {S02 CP8F} % Usage (list ones you are aware of).
        {Christos Kapoutsis, S02} % Last revision info (author, date).

\begin{problem} An adequately-prepared 6.042 student has
the following texts:

\begin{itemize}
\item 5 copies of Velleman
\item 2 copies of Rosen, 3rd edition
\item 6 copies of Rosen, 4th edition
\item 4 copies of the Spring '10 Lecture Notes
\end{itemize}

Copies of the same text are indistinguishable.  The student also has
a bookshelf with four distinguishable shelves.  In how many different
ways can the student arrange his texts on his bookshelf?  Assume that
each shelf has enough space to hold all of the texts and that two
arrangements are different if the texts appear in a different order on
a shelf.

\solution{Each arrangement of the texts on the bookshelf corresponds to
a sequence of the texts together with three ``dividers''.  The texts on
the first shelf appear in the sequence before the first divider, the texts
on the second shelf appear between the first and second dividers, etc.
Thus, the number of different arrangements is $\displaystyle
\binom{20}{5,2,6,4,3}$.
}
\end{problem}
