METU Department of Mathematics Math 405 Combinatorics Spring 2010

QUIZ 4

Problem 1. Five houses should be painted in three colors so that all the colors are used. In how many different ways it can be done ? (Explain how you calculate and find the answer.)

Problem 2. Express the coefficients at x^{k} in the product x(x + 1)(x + 2)(x + 3) as the Stirling numbers. Calculate these coefficients.

Problem 3. Give the recursive formulas for the Stirling numbers of the first and second kinds.