\problemdata      
        {?} % latex-friendly label for the prob.
        {Counting} % The topic(s) of the problem content.
        {?} % Source (if known)
        {Fall 2001, PS8} % Usage (list ones you are aware of).
        {Christos Kapoutsis, S02} % Last revision info (author, date).


\begin{problem}
{\bf In a Bostonian field of dreams...}
In some imaginary world, the Boston Red Sox are playing the New York Yankees
for the World Series Championship title.  In fact, they've already won the first
game of the series, and there is great enthusiasm in Beantown at the prospect
of winning the whole thing.  People in the sports bars talk excitedly about 
the different ways Boston could win (will they sweep it?  will they lose the 
second game but come back and take the next three? ...), but they are all a 
little too inebriated
to figure out all the possibilities.  Wielding your tree diagram method and
your smart MIT brainpower, 
calculate for them
the many many different ways the Red Sox could actually take home the title!  
(For those
of you unfamiliar with baseball, the World Series is a best of seven tournament, 
i.e. the first team to win four games wins the title.)

\solution{The required
\href{http://theory.lcs.mit.edu/classes/6.042/fall01/figures/tree-psol8.jpg}{tree
diagram} is attached.

Alternatively, one can
count the number of ways the Red Sox could win using the combinatorics we have
covered since last week.  We need to choose three games out of six remaining for
the Red Sox to win.  After each third game is played in which the Red Sox win, 
the series is considered over.  Thus, there are $C(6,3) = 20$ possibilities.
}

\end{problem}
