COM209 Engineering Mathematics V September 2020 Tutorial 1 1. A computer virus erases files from a disk drive in random order. If there are 10 files on the disk, in how many different orders can 5 files be erased from the drive? 2. Suppose that to send an Internet packet from the east coast of the United States to the west coast, a packet must go through a major east-coast city (Boston, New York, Washington, or Atlanta), a major mid-west city (Chicago, St. Louis, or New Orleans), and a major west-coast city (San Francisco or Los Angeles). How many possible routes are there? 3. Traditionally, computers use binary arithmetic, and store n-bit words composed of zeros and ones. The new m-computer uses m-ary arithmetic, and stores n-symbol words in which the symbols (m-ary digits) are from the set {0, 1, . . . , m − 1}. How many n-symbol words are there with k0 zeros, k1 ones, k2 twos, ..., km−1 copies of symbol m−1, where k0 +k1 +k2 +...+km−1 = n? 4. The following is taken from Gubner’s “Probability and Random Processes for Electrical and Computer Engineers”. 5. Discussion of problems from Ross: 2.2, 2.4, 2.12.