An urn contains 1 red ball, 2 green balls, and 6 blue balls. Three balls are randomly chosen from the urn. How many different color combinations are possible?

Question

A.
8
B.
7
C.
6
D.
2

Answer 1

To determine the different color combinations possible when choosing 3 balls from the urn containing 1 red ball, 2 green balls, and 6 blue balls, we will analyze the possible scenarios based on the colors of the balls chosen.

1. Combination breakdown:

Let's denote:

• R = Red
• G = Green
• B = Blue

The possible combinations based on the number of each color chosen can be analyzed as follows:

1. All balls of the same color:

   • It is impossible to choose 3 balls of the same color because:
     • There is only 1 red ball.
     • There are only 2 green balls.
     • There are 6 blue balls, but they are not all the same color since there would only be blue balls if they are all the same.

2. Two balls of one color and one ball of another:

   • 2 Blue, 1 Green: (B, B, G)
   • 2 Blue, 1 Red: (B, B, R)
   • 2 Green, 1 Blue: (G, G, B)

3. One ball of each color:

   • 1 Red, 1 Green, 1 Blue: (R, G, B)

2. Summary of combinations:

• (B, B, G)
• (B, B, R)
• (G, G, B)
• (R, G, B)

Counting all distinct combinations gives us a total of 4 combinations:

1. (B, B, G)
2. (B, B, R)
3. (G, G, B)
4. (R, G, B)

Thus, there are 4 different color combinations possible when choosing 3 balls from the urn.

The answer choices provided (8, 7, 6, 2) do not include 4. However, based on our working, we can confidently conclude that the different color combinations are 4. Please check that the answer choices from where this problem was taken are correct or if more options should be listed.