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.)
W.
X.
Y.
Z.
A.
Y
B.
W
C.
Z
D.
X
W.
X.
Y.
Z.
A.
Y
B.
W
C.
Z
D.
X
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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.
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.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.