Week 2 Problem Session: Counting practice

The second Problem Session — deriving the week 2 combo and class counts by hand, then reusing the technique on a smaller counting problem

1 March 2027

Before the session#

Read the week 2 lecture and attempt the 1,326/169 derivation yourself before seeing anyone else’s version of it. Bring whichever step you got stuck on, if any — a wrong attempt is more useful to compare than a blank page.

In the session#

The group rebuilds the combo and class counts together, case by case: pairs, suited hands, offsuit hands, checking at each step that the running total still adds to C(52, 2). Getting the case split right — deciding what counts as a separate case at all — turns out to be the actual skill; the arithmetic inside each case is easy once the split is correct.

Then the same technique gets pointed at a smaller, un-answered question: how many three-card flops contain at least one ace? This isn’t marked and isn’t in the lecture, but it’s the same counting move week 3 needs, applied somewhere the answer isn’t already known going in.

Afterwards#

Nothing is marked this week. What should be settled going into week 3: fluent use of C(n, k), and the combo/class distinction from lecture.