A mini license plate for a toy car must consist of a number followed by two letters. Each letter must be a C, A or R. Each number must be a 3 or 7. Repetition of letters is permitted.

Question

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 a C. Give solution exactly in reduced fraction form.

Answer 1

2 choices for the number, followed by 3x3 choices for the letters
number of plates = 2x3x3 = 18

the second part is somewhat ambigious.
Can both spots be C ? I will assume that

1. one C = 2x1x2 + 2x2x1 = 8
2 two C;s = 2x1x1 = 2

number of cases = 10

prob of a C = 10/18 = 5/9

Answer 2

SO CONFUSED STILL....

Answer 3

3CC
3CA
3CR
3AA
3AC
3AR
3RR
3RA
3RC , that's 9 now do the ones starting with 7 for another 9
for a total of 18

now count how many of those 18 have a C in them .
Including the column starting with 7, I count 10 with a C in them

What part is still confusing?

Answer 4

okay...i get it now thank you Reiny :)