Archive for May, 2010
ordinals on wall street. via mitchell near atwater.
much of the point here is to “explain why”
the figure in the upper right… “pascal’s triangle”…
works the way it does: students gladly learn
in minutes how to write out rows by adding
pairs taken from previous rows (according to
the formula in the lower left, though they
know it not; eventually they’ll have to be
encouraged to care but of course one need
not speak of thorny notational issues at
every single opportunity; when the student
is ready the code’ll have been there waiting
all along). the thing is: what the heck does
this ritual-adding-together have to do
with “counting subsets”, then, eh? because
when we “use” these numbers in our little
probability-and-counting problems back
in class, we’ll be referring to “N choose R”
all the time: the number of ways to
“choose” a set of R things from a set of N.
well, put like that…
the thing is more or less obviously
then to look carefully at arrangements-of-subsets
and see if we can piece out
“what comes from where”.
my best shot so far.
better with the handwaving of course.