Sample space: marbles Given a bag of 5 different colour marbles: R, G, B, W, Y, we need to create a sample space to
study the outcome of when 3 marbles are picked out of the five marbles in the bag.
The way I approached this, is that since we are creating a sample space for 3 marbles picked
out of 5, then there is 5 choose 3 ways to make the selection.
Therefore, 5 choose 3 = 10 = {(RGB), (RGW), (RGY), (RBW), (RBY), (RWY), (GBW), (GBY), (GWY), (BWY)}

Have I done this correctly?
 A: Imagine that you put your five marbles on a table in front of you, in any way, and that you have 3 small boxes you want to fill with one marble in each box.
In the first box, you could put any of the 5 marbles. In the second box, you could put any of the 4 marbles left, and in the third box, you could put any of the 3 marbles left. Now, for each of the 5 marbles you can put in the first box, there are 4 possible choice of marbles for the second box, thus you have $5\times4$ possibilities. For each of the different ways you can put marbles in the first and second box, there are 3 possibilities for the third box. Therefore, you have $5\times4\times 3 = 60$ different ways you can put 5 marbles into 3 box. Also notice that the order matters in this example. You could have (RGB) and (RBG) as being different.
To get the number of different possibilities when the order doesn't matter, i.e. that (RGB) is equivalent to (RBG), you want to divide the result we just found by the number of equivalent ways you can place the three boxes. You can use the same reasoning as before, but this time trying to find the different ways you can place 3 boxes out of 3 boxes.
If you put back each marble on the table after putting in in one box (recording where it went), then in the first box there could be any of the 5 marbles, in the second box there could be any of the 5 marbles and in the third box there could also be any of the 5 marbles. How many different possibilities does that make?
A: Yes, as long as the order of appearance does not matter.
