Question

A soccer tournament assigns a unique two-color uniform to each team using the colors Red, Blue, Green, and Yellow. Each uniform is mostly one color with a different colored stripe. Write an organized list using the format (main color, stripe color) to represent the sample space. Does it matter what order you list the different ways to assign the uniform colors? Explain your reasoning.

Answer 1

The order of listing unique two-color combinations for soccer uniforms doesn't affect the completeness of the sample space but a systematic listing ensures no combination is missed and enhances clarity.

Step-by-step explanation:

To create an organized list representing the sample space for a soccer tournament where each team has a unique two-color uniform composed of main and stripe colors from the set of Red, Blue, Green, and Yellow, we pair each color with every other color in a stripe role while excluding pairs where the main and stripe color are the same. The resulting combinations are as follows:

• (Red, Blue)
• (Red, Green)
• (Red, Yellow)
• (Blue, Red)
• (Blue, Green)
• (Blue, Yellow)
• (Green, Red)
• (Green, Blue)
• (Green, Yellow)
• (Yellow, Red)
• (Yellow, Blue)
• (Yellow, Green)

The order in which you list these combinations does not matter with respect to the sample space's completeness and correctness. However, a systematic method of listing can make it easier to ensure that no possible combination is overlooked, and it can improve the clarity of communication when describing the sample space to others.