Emilio has 6 red buttons, 1 green button, and 2 black buttons in a jar. Which list shows all the possible unique outcomes if Emilio chooses 3 buttons at one time from his jar? (Note: One outcome is shown per row in the tables.)

Question

W.
X.

Y.
Z.
A.
Y
B.
W
C.
Z
D.
X

Answer 1

To find all the unique outcomes when Emilio chooses 3 buttons from the jar, we need to consider the different combinations he can draw from the 6 red buttons, 1 green button, and 2 black buttons. The different combinations can include buttons of different colors as well as repeated colors due to having multiple red buttons.

Given:

• Red buttons: 6
• Green buttons: 1
• Black buttons: 2

We can categorize the possible combinations based on the color and number of buttons:

1. All buttons of one color:

   • 3 Red buttons: RRR

2. Two buttons of one color, one button of another:

   • 2 Red, 1 Green: RRG
   • 2 Red, 1 Black: RRB (can have 2 ways: BB/RRB or RB/RBB)
   • 1 Red, 2 Black: RBB

3. One button of each color:

   • 1 Red, 1 Green, 1 Black: RGB (can vary based on which black button is chosen, but since they are identical, they count as one)

Collectively, the unique combinations can be detailed as:

• RRR
• RRG
• RRB (can be abbreviated to RRB since blacks are identical)
• RBB
• RGB

Now, let's enumerate the possible unique outcomes:

1. RRR
2. RRG
3. RRB
4. RBB
5. RGB

Now we can identify if the lists W, X, Y, Z contain these combinations or some other combinations that Emilio could possibly draw. However, you did not provide the lists W, X, Y, and Z. Please share them, and I can help match the combinations listed above with one of these lists.