[Math] Combination of Colors

Question

So I have 11 colors (blue, purple, pink, green , gray, white, black, brown, orange, yellow, red) and I want to know how many different combinations I could have? For example, some combinations would be: red, blue, and green; red and brown; all the colors; red; blue, pink, purple, white, and black.

Answer 1

Each color may or may not be included. So for each color, there are two choices (include, don't include). The number of combinations that are possible, including no colors at all, is then $$\underbrace{2\cdot 2 \cdot 2\cdot \cdots \cdot 2}_{\large 11 \text{ times}} = 2^{11}.$$

If you must use at least one color, then the combinations total $2^{11} - 1$.