A 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

A 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.

amistre64 · Answer

78 c     87 c     97 c
78 a     87 a     97 a
78 r      87 r     97 r

79 c     89 c     98 c
79 a     89 a     98 a
79 r      89 r     98 r

amistre64 · Answer

18 total ; and 6 have an r

6/18 = 1/3 = .3334

anonymous · Answer

so the first one is the tree diagram?

amistre64 · Answer

i got no way of making a tree diagram .... 

that is the sample space; teh result of all possible outcomes

anonymous · Answer

ok

amistre64 · Answer

the counting principle is:

3*2*3 = 18 different ways to set it up; and our sample space shows that

anonymous · Answer

so when i go to make a tree diagram how would i do it? put the 78 c 87 c 97 and other numbers in the diagram

anonymous · Answer

Since it states that it can not be repeated the first number has 3 possibilities, the 2nd spot can only be chosen out of 2 because repetition is not allowed, the final spot can be any 3 of the letters. So, you take the possibilities to calculate the number of out comes: 3*2*3 = 18.

In order to create a tree diagram create 3 columns, with any possibility of variables. 
EX:
7       7       C
8       8       A
9       9       R

then draw lines starting with the first column first row: 7. since repetition is not allowed, a line can only be drawn to 8 and 9. then from 8 lines can be drawn to C,A,R, also from 9 lines can be drawn to C, A, R, as well. Then repeat going down the first column. When you reach the end of the first column you have drawn all possibilites.

anonymous · Answer

ok im a little confused ... so my top line would be the  7 8 9? and then Put a 3 lines? that would be C A R from each number?

amistre64 · Answer

attachment

anonymous · Answer

The provide attachment sent by amistre64 is more of a tree.Mine just has the branches super imposed on itself.

amistre64 · Answer

this is all the possible paths to take to get answers; the tips are how many outcomes

anonymous · Answer

oh ok.... :)