Final answer:
Bred can paint the wall in 6 different ways using 8 horizontal stripes, considering a maximum of 2 colors out of blue, red, and white with enough paint for 5 stripes of each color.
Step-by-step explanation:
The question at hand involves combinatorics, which is a branch of mathematics dealing with combinations and permutations. Bred can paint a wall with 8 horizontal stripes using at most 2 colors from the options of blue, red, and white, with enough paint for 5 stripes of each color. Since he is using at most 2 colors, we need to calculate the number of combinations for each pair of colors as well as the individual colors. The possible pairs with their respective numbers of combinations are blue-red, blue-white, and red-white. For blue-red and blue-white, he can paint 5 blue stripes and 3 stripes of the other color, while for red-white, he can paint 5 red stripes and 3 white stripes.
The combinations for each pair would be:
Blue-Red: 5 blue + 3 red
Blue-White: 5 blue + 3 white
Red-White: 5 red + 3 white
Additionally, Bred can choose to use only one color. Thus, for each of the colors blue, red, and white, there will only be one way to paint the wall.
Therefore, the total different ways Bred can paint the wall are the sum of the combinations for each pair plus the individual color options:
For pair Blue-Red: 1 way
For pair Blue-White: 1 way
For pair Red-White: 1 way
Only Blue: 1 way
Only Red: 1 way
Only White: 1 way
Adding these up gives us a total of 6 different ways to paint the wall.