FINITE MATHEMATICS FOR THE SOCIAL AND MANAGEMENT SCIENCES Math 1051-11 Fall 2017 CRN: 80237 HOMEWORK V DUE Wednesday, December 6, at the beginning of the lecture 1. 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 4-pick has ... (a) at least 2 green marbles. (b) all three colors represented. (c) at most two colors represented. 6 points Work your probabilities out completely, leaving them as fractions in their simplest form. 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 ... (a) Has four A's. (b) Has at least two A's. (c) Begins and ends with an A. 7 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 mn , Pnm , Cnm , and factorials. 3. Of the 9-letter passwords formed by rearranging the letters AAAABBCCC, I select one at random. Determine the probability that my password ... (a) Is a palindrome. (b) Has A in the middle. (c) Begins and ends with B. (d) Has no two C's next to each other. You may leave your probabilities in terms of mn , Pnm , Cnm , and factorials. *************************************** DON'T FORGET OUR FINAL EXAM: WEDNESDAY, DECEMBER 13, 10:20 TO 12:20 IN OUR USUAL LECTURE ROOM 7 points