Worksheet 9
MAT 1000
Wayne State University
Due: 2/25-2/26
In the board game Risk, players throw three 6-sided dice at once.
1. How many possible outcomes are there? (Don’t try to list them all.)
All of these outcomes are equally likely.
2. What is the probability that all three of the dice will show the same number? (You can easily list
all of the outcomes in this event.)
3. What is the probability that all three dice show a 3 or less? (You will not be able to list all of the
outcomes in this event—find a different way to count them.)
A computer system requires passwords of 5 characters, which can be only lower case letters.
4. How many possible passwords are there?
5. What’s the probability that someone could guess a password with just one attempt?
A different system requires passwords of only 4 characters, but each character can be either a number
or a lower case letter.
6. How many possible passwords are there?
7. What’s the probability that someone could guess a password with just one attempt?
8. Based on your answers to problems 5 and 7, which of the two systems is more secure? Why?
9. A hospital wants to fill three nursing positions. Position 1 is the day nursing supervisor, position
2 is the night nursing supervisor, and position 3 is the nursing coordinator position. There are 15
candidates, all qualified to fill any of the three positions. Determine the number of different
ways the positions could be filled by these applicants.
10. A dinner table has 8 seats. In how many ways 8 people can be seated at the table?