Understanding the Problem
To determine the possible ratios of black to white marbles in a collection of 10 marbles, we need to consider the total number of marbles and how they can be divided into two categories: black and white.

Possible Ratios of Black to White Marbles
Given that there are 10 marbles total, let’s denote the number of black marbles as B and white marbles as W. The equation we can use is:
- B + W = 10
This means the number of black marbles can range from 0 to 10, while the number of white marbles will decrease correspondingly.

Exploring Ratios
The ratio of black to white marbles can be expressed as:
- Ratio = B : W
Using the total of 10 marbles, the possible ratios can be calculated as follows:
- If B = 0, W = 10, Ratio = 0 : 10 (or undefined)
- If B = 1, W = 9, Ratio = 1 : 9
- If B = 2, W = 8, Ratio = 2 : 8 (or 1 : 4)
- If B = 3, W = 7, Ratio = 3 : 7
- If B = 4, W = 6, Ratio = 4 : 6 (or 2 : 3)
- If B = 5, W = 5, Ratio = 5 : 5 (or 1 : 1)
- If B = 6, W = 4, Ratio = 6 : 4 (or 3 : 2)
- If B = 7, W = 3, Ratio = 7 : 3
- If B = 8, W = 2, Ratio = 8 : 2 (or 4 : 1)
- If B = 9, W = 1, Ratio = 9 : 1
- If B = 10, W = 0, Ratio = 10 : 0 (or undefined)

Conclusion
The ratio of black to white marbles can vary widely, but it becomes impossible to have a ratio of black to white marbles that does not conform to the values derived from the equation B + W = 10. For example, a ratio of 7 : 4 could not exist since it does not yield a whole number of marbles when totaled to 10.
Thus, the answer will depend on the context provided but must adhere to the total of 10 marbles and valid ratios derived from it.