Question

A box has three cards numbered 1, 2, and 3

Answer 1

Answer:

{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}