We discussed various practice problems for test 3. The cards problems have to be done carefully by splitting the counting process into steps, and trying to keep in mind the restrictions imposed on ranks and suits.

Wikipedia has a list of all the poker hands with their probability. As an exercise, try to compute each one yourself, then compare your answers to the article. Remember that the stronger hands must be excluded, i.e. a pair means exactly a pair, not two pairs or three of a kind.

The formula I wrote on the board to count the number of ways to choose k elements out of n with replacement when order does not matter is correct, only the role of n and k are reversed compared to what is written in the class notes (sorry about the confusion). Try to remember where the formula comes from rather than learning it by heart.