SOLUTION: Oh please help me, this problem has almost made me cry. I am a 34 year old student and can't even begin to understand this.. A mini license plate for a toy car must consist of

Question 266657: Oh please help me, this problem has almost made me cry. I am a 34 year old student and can't even begin to understand this..
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. Repetitions of letters is permitted.
there are 4 parts to this:
1. Use the counting principle to determine the number of points in the sample space.
2. Construct a tree diagram to represent this situation.
3. List the sample space.
4. Determine the EXACT probability of creating a mini license plate with a C. Give the solution in reduced fraction form.
Please show me everything, I have 7 other problems to do like this and I need alot of help please, I am taking online courses and my professor isn't helping much at all.
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
First our license plate must be in the form of
# - L - L,
or,
number - letter - letter.
we have 2 choices for the numbers, 3 or 7
we have 3 choices for the letters c - a - r.
repetition is allowed: So there is a second 3 choices for letters c - a - r
---
1. Use the counting principle to determine the number of points in the sample space.
ANSWER: The counting principal is all about multiplying the number of ways one event occurs x the number of ways a second event occurs x the number of ways a third event occurs and so on. In our case we have 2 number choices and 3 letter choices, but two times.
2 x 3 x 3 = 18.
---
2. Construct a tree diagram to represent this situation.
ANSWER:
step 1 - write a 3 and below it with a little space write a 7
step 2 - from the 3 draw 3 arrows and next to the end of these write c, a, r
step 3 - next to each of the letters draw another 3 arrows and write the letters again for c, a, r
step 4 - from the 7 draw 3 arrows and next to the end of these write c, a, r
step 5 - next to each of the letters draw another 3 arrows and write the letters again for c, a, r
---
3. List the sample space.
ANSWER: this is pretty straight forward from the tree diagram. we get
3aa, 3ab, 3ac, 3ba, 3bb, 3bc, 3ca, 3cb, 3cc,
7aa, 7ab, 7ac, 7ba, 7bb, 7bc, 7ca, 7cb, 7cc.
3ab plate is different from 3ba plate
---
4. Determine the EXACT probability of creating a mini license plate with a C. Give the solution in reduced fraction form.
ANSWER: 3ac, 3bc, 3cc, 3ca, 3cb, 7ac, 7bc, 7cc, 7ca, 7cb
"with a C" means to me one or two C"s in any order.
P(C) = 10/18 = 5/9.
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