FINITE MATHEMATICS FOR THE SOCIAL AND MANAGEMENT SCIENCES Department of Mathematics, George Washington University Math 1051 Fall 2018 HOMEWORK V DUE Thursday, November 29, at the beginning of the lecture 1. Work the following probabilities out completely, leaving them as fractions in simplest form: (8)31-Pf-Cg5l-Cg 5! - o; (b) A bag contains 6 marbles: 1 red, 2 blue, and 3 green; I reach into the bag and pick 4 marbles (simultaneously) at random. Determine the probability that my 4pick includes marbles of at most two different colors. (c) I select, at random, three dishes, not necessarily different, from the nine dishes on a menu. Determine the probability that at least two of the dishes are the same. Leave your pmbobiiities as fractions in simpiest form. 6 points 2. Of the 7-digit passwords formed by mixing 3 numbers (chosen from 1 to 9, without repeats) and 4 letters (chosen from A to Z, allowing repeats), I pick one at random. Determine the probability that my password (3) Has four A's. (b) Has at least two A's. (c) Begins and ends with an A. 6 points (d) Has two numbers next to each other with the third one not next to them. You may leave your probabilities in terms of m\