10. At a sandwich counter, a customer can choose from among the following fillings: bacon and egg, Hungarian sausage, bologns, cheese, and chicken. He can choose from among the following toppings: pickle relish, tomato, coleslaw, or cucumber, and from among the following dressings: thousand island. mayonnaise, ranch, or mustard.

a. In how many ways can a customer order a sandwich from this counter?

11. A teacher gave a quiz consisting of a five-item matching test and a five-item multiple choice test with four choices each. If a student answers each question in the quiz, in how many ways can he answer the questions?

12. Camille and Clarisse play a game of Scissors, Paper, and Stone. where each player imitates a pair of scissors, a sheet of paper, or a piece stone with her right hand. Ar a signal, the two players will simultaneously imitate one of these three objects. Scissors beat paper, paper beats stone, and stone beats scissors. There is a tie if the two players choose the same object. Assume that each girl is equally likely to choose from among the three hand signals.

a. Construct the sample space for one round of this game.

13. During the opening ceremonies of an international mathematics competition, 4 Chinese, 3 Japanese, 5 Korean, and 4 Singaporean participants are to be seated in one row, such that representatives from the same country sit next to each other.

a. In how many ways can the 16 participants be seated?

b. If two of the Chinese participants are brothers and prefer to sit next to each other, how many seating arrangements are possible? ​