Compulsory assignment (Session 3)
The following problems form the compulsory assignment to be presented in Tuesday class. Please see the web pages for details. All answers must be justified.
Problem 6.1 You are hosting a panel discussion, with three people on the panel, named Alice, Bob, and Charlie. Write down every possible seating arrangement of these three on the three seats on the stage (from left to right, say).
Explain how you ensure that no combination is forgotten.
Problem 6.2 How many distinct poker hands (five cards) can be drawn from a 52-card deck?
Problem 6.3 The student chess club has 66 male and 37 female members. They have to elect a president and a vice-president, where the two have to have different genders. How many different combinations of president and vice-president can be formed in the club?
Problem 6.4 In a tiny Chinese resturant, the chef has a repertoire consisting of three sauces (Hoisin, Szechuan, and Satay), either steamed rice, fried rice, or noodles, and either chicken or pork. A dinner should consist of one kind of meat, one source of starch (rice/noodles), and one sauce. How many distinct dishes can he put on the menu?
Problem 6.5 Calculate the following
- .
Problem 6.6 Consider two sets and of size and respectively. How many ordered pairs exist, so that and .