Step 1 :The problem is asking to find the sample space of the probability experiment and determine the number of outcomes in the sample space when randomly choosing a number from the multiples of 3 between 1 and 20.
Step 2 :The multiples of 3 between 1 and 20 are 3, 6, 9, 12, 15, and 18.
Step 3 :So, the sample space is \{3, 6, 9, 12, 15, 18\}.
Step 4 :The number of outcomes in the sample space is the number of elements in the sample space.
Step 5 :Final Answer: The sample space is \{3, 6, 9, 12, 15, 18\}. There are \(\boxed{6}\) outcomes in the sample space.