Two faces of a six-sided die are painted red, two are painted blue, and two are painted yellow. The die is rolled three times, and the colors that
appear face up on the first, second, and third rolls are recorded.
(a) Let BBR denote the outcome where the color appearing face up on the
first and second rolls is blue and the color appearing face up on the third
roll is red. Because there are as many faces of one color as of any other, the
outcomes of this experiment are equally likely. List all 27 possible outcomes.
(b) Consider the event that all three rolls produce different colors. One outcome
in this event is RBY and another RY B. List all outcomes in the event.
What is the probability of the event?
(c) Consider the event that two of the colors that appear face up are the same.
One outcome in this event is RRB and another is RBR. List all outcomes
in the event. What is the probability of the event?

Let’s say you play a game with the dice from question 1. The game consists of rolling the dice 3 times. If all three rolls are of the same color you win $8. If two of the three rolls are of the same color you win $4. If all three rolls are different colors you lose $5. Determine if this game is fair. Do this finding the expected value. Would you play this game? Why or why not?

A teacher gives a test with 21 questions. Students are allowed to
choose any nineteen to answer. How many different choices of thirteen questions
are there?
(a) How many ways can the letters of the word P AT CHW ORK be arranged
in a row?
(b) How many ways can the letters of the word P AT CHW ORK be arranged
in a row if P and A must remain together (in order) as a unit?
(c) How many ways can the letters of the word P AT CHW ORK be arranged
in a row if the letters W OR must remain together (in order) as a unit?