To determine how many different colors Frank can create by mixing the secondary colors, let's first identify the secondary colors. The traditional secondary colors are green, orange, and purple.
If Frank combines these secondary colors, he can create:
- Green + Orange
- Green + Purple
- Orange + Purple
These combinations can produce new colors, but the question does not specify the outcomes of these mixes, so we focus on the combinations themselves.
Since there are three secondary colors and each pair can be combined, the number of unique pairs of combinations can be calculated using the formula for combinations:
\[ \text{Combinations} = \binom{n}{r} = \frac{n!}{r!(n-r)!} \]
Where \(n\) is the total number of items (secondary colors), and \(r\) is the number of items to choose (2, for a pair).
For \(n = 3\) and \(r = 2\):
\[ \binom{3}{2} = \frac{3!}{2!(3-2)!} = \frac{3 \times 2 \times 1}{2 \times 1 \times 1} = 3 \]
Thus, Frank can create 3 different unique combinations of secondary colors by mixing them together.
Therefore, the answer is 3.
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