Discrete Structures Test 3 Sample Questions

I would take the following questions "with a grain of salt."  They are taken from a different semester when I taught things in a different order.  These questions were only half of the exam, so you can expect a few additional questions. 

1. (5 points)  A video game on a microcomputer is begun by making selections from each of three menus.  The first menu (number of players) has four selections, the second menu (level of difficulty) has eight, and the third menu (speed) has six.  In how many configurations can the game be played?

2. (5 points)  A, B, C, and D are nodes on a computer network.  There are two paths between A and C, two between B and D, three between A and B, and four between C and D.  Along how many routes can a message from A to D be sent?

3. (10 points)  Nineteen different RAM chips are available for use in a computer.  They make the following claims:  12 claim to be fast, 10 claim to be durable, 11 claim to be inexpensive, 5 claim to be both fast and durable, 6 claim to be both fast and inexpensive, and 5 claim to be both durable and inexpensive.

• How many chips make all three claims?

• How many chips claim to be fast but do not claim to be inexpensive?

4. (5 points)  Stock designations on an exchange are limited to three letters.  How many different designations are there?

How many different designations are there if letters can’t be repeated?

5. (5 points) In how many unique ways can the letters in the word BANANA be arranged?

6. (10 points)  Three coins are tossed at the same time, each equally likely to come up heads or tails.

·        What is the size of the sample space?

·        What is the probability of getting one head and two tails?

·        What is the probability of getting all tails?

·        What is the probability of getting all heads or all tails?

• What is the probability of getting all heads and all tails?