At the coffee station at work, you have several options when making a cup of coffee. You can choose to add no cream (N), regular cream (R), or hazelnut-flavored cream (H). You can also choose to add no sweetener (O), sugar (S), or aspartame (A).

a) Determine the number of points in the sample space.

b) Construct a tree diagram and list the sample space.

If you were to randomly prepare one cup of coffee, determine the probability that

c) You prepared a cup of coffee with regular cream and sugar?

d) You prepared a cup of coffee with no cream and no sweetener?

e) You prepared a cup of coffee with sugar?

Use the fundamental counting principle to determine the answer to part (a). Assume that each event is equally likely to occur.