1) Suppose the problem statement is as follows. Roll two 6 sided dice and add the numbers on the faces. What is the total sample space S (A sample space is the set of all possible outcomes)? If we define an event A as all numbers between 3 and 9, what is the set defining A?
2) The combination of a number lock is given by 3 numbers from the set {0, 1, ..., 59}. Find the number of combinations possible.
3) A dinner party is attended by four men and four women. How many unique ways can the eight people sit around the table? How many unique ways can the people sit around the table with men and women alternating seats?
4) A hockey team has 6 forwards, 4 defensemen, and 2 goalies. At any time, 3 forwards, 2 defensemen, and 1 goalie can be on the ice. How many combinations of players can a coach put on the ice?
5) A hot dog vendor provides onions, relish, mustard, ketchup, Dijon ketchup, and hot peppers for your hot dog. How many variations of hot dogs are possible using (a) one condiment? (b) Two condiments? (c) No condiments? (d) all of the condiments?