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Unformatted text preview: Homework 2 The following homework set has two types of problems. Those labeled SS are self-study problems that do not need to be turned in. However, there are problems that I suggest you complete to ensure that you understand all the material in the class. The problems not labeled SS should be submitted for a grade. In general, the SS problems are easier than the graded problems, so they can be used to practice and build expertise before doing the graded problems. On-campus students: Submit non-SS problems by class time on Wednesday, September 21st. No electronic submissions will be accepted. Off-campus students: Submit non-SS problems via Sakai by Wednesday, September 28th. Combinatorics Use combinatorics to solve the following problems: SS-1. Find the number of possible combinations for a combination lock that has a combination consisting of three numbers from the set 160. Find the number of combinations under these three scenarios: (a) The lock is a traditional combination lock consisting of a rotating dial that can be pointed to any of 60 different numbers in a specific order. Depending on the mechanical implementation of the lock, repeats may or may not be allowed. Lets assume that we can have repeats. (Answer: 216,000) (b) Now assume we have the same type of lock, but the implementation is such that repeats are not allowed. (Answer: 205,320) (c) Now suppose we have a different type of combination lock. For instance, one with 60 push buttons, where the lock opens if you push in the three correct buttons. Now order doesnt matter and repeats are not allowed. (Answer: 34220) SS-2. (a) How many ways can 3 boys and 3 girls sit in a row? (Answer: 720) (b) How many ways can 3 boys and 3 girls sit in a row if the boys and the girls are each to sit together? (Answer: 72) (c) In how many ways if only the boys must sit together? (Answer: 144) (d) In how many ways if no two people of the same sex are to sit together? (Answer: 72) 1. Calculate the probabilities of winning the first four prizes (the Grand Prize through the $100 prize) of the Powerball lottery (see http://www.powerball.com/powerball/pb prizes.asp ) and verify if the posted probabilities (under the erroneous title Odds) are correct. SS-3. Two cards are randomly drawn from an ordinary playing deck. What is the probability that they form a blackjack? That is, what is the probability that one of the cards is an ace and the other one is either a ten, a jack, a queen, or a king? (Answer: 128/2652) SS-4. Poker dice is played by simultaneously rolling five dice. show thatSS-4....
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This note was uploaded on 01/29/2012 for the course ECE 101 taught by Professor Wang during the Spring '11 term at Iowa State.
- Spring '11