Discrete mathematics elementary and beyond by Laszlo Lovasz, Jozsef Pelikan, Katalin L. Vesztergombi

4. State a theorem or algorithm from the textbook that could be used to solve each of the following problems. (You do not need to actually solve them.) (a) Find the coefficient of a0640 in the expansion of (a + b)50. (b) Find the cheapest way to connect 32 cities with power lines. (c) Find the number of labeled trees on 100,000,000 nodes. (d) Determine the number of times you need to flip a coin in order to have a 99% probability that between 49% and 51% are heads.