mini license plate for a toy car must consist of two numbers followed by a letter. Each number must be a 7, 8 or 9. Each letter must be a C, A or R. Repetition of digits is NOT permitted.
Use the counting principle to determine the number of points in the sample space.
Construct a tree diagram to represent this situation:
List the sample space.
Determine the exact probability of creating a mini license plate with an R. Give solution exactly in reduced fraction form.

Question

mini license plate for a toy car must consist of two numbers followed by a letter.  Each number must be a 7, 8 or 9. Each letter must be a C, A or R. Repetition of digits is NOT permitted.
Use the counting principle to determine the number of points in the sample space. 
Construct a tree diagram to represent this situation:
List the sample space. 
Determine the exact probability of creating a mini license plate with an R. Give solution exactly in reduced fraction form.

anonymous · Answer

how many elements in the sample space comes from the counting principle 
you have $3\times 2=6$ choices for the letters, then 3 choices for the numbers. so there is a total of $6\times 3=18$ possible license plates

anonymous · Answer

you can draw the tree if you like, but one third of the plates will contain the letter R