1. Suppose you have a collection of 40 books. What would 40!, 40 P 10, and 40 C 5 count in the context of the 40 books? Give an example of when each of the previous counting techniques would be applicable.
2. A friend of yours created the following game: Each player will take turns rolling two dice. If the sum of the dice is odd, the player gains one point. If the sum of the dice is even, the player loses one point. The first player to score 100 points wins. Verify that the expected value of the player’s score after playing one round of the game is zero (recall that there are 36 possible outcomes when rolling two fair dice). What does this expected value mean in context and does it indicate a problem with the proposed game?