Abox has three cards numbered 1, 2, and 3
a bag has three balls labeled a, b, and c
shen will randomly pick a card from the box and record the number chosen.
then he will randomly pick a ball from the bag and record the letter chosen.
give the sample space describing all possible outcomes.
then give all of the outcomes for the event that the letter chosen is c.
use the format 1 a to mean that the number chosen is 1 and the letter chosen is a.
if there is more than one element in the set, separate them with commas.

{1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}

{1C, 2C, 3C}

Step-by-step explanation:

First is all possibilities.  Let's do it one step at a time.  The first step is the number, what are all the numbers that can be chosen?  1 2 and 3.  then, when you pick1, what are all the letters that can be chosen?  A B and C.  Do this for 2 and 3 and you get all possibilities.

{1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}

When you have steps like this you can multiply the number of results to get the total number of possibilities as well.  Step one has 3 results, step 2 has 3 results, that means there are 3*3 total, which is 9.  Do be careful it matches this  kind of setup, where the step 2 is the same for all step 1s.  So if instead if you got 1 for step 1 you picked from a bag with 3 things, then for 2 you picked from a different bag with a different number, that multiplication trick wouldn't work.

Now just pick throught he sample space to find all with C.  There are three, {1C, 2C, 3C}

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.