Question 1) State an analogue of Vandermonde's convultion for multinomial coefficients, and use a combinatorial argument to establish it.
Question 2) Suppose that a museum curator with a collection of n paintings by Jackson Pollack needs to select k of them for display, and needs to pick m of these to put in a particular prominent part of the display. Show how to count the number of possible combinations in two ways so that the cancellation identity appears.