To determine the Miller indices of a plane in a cubic structure that contains all the directions [100], [011], and [111], we can follow the steps outlined below:

1. Understand the cubic structure:
- A cubic structure has three mutually perpendicular axes, labeled as x, y, and z.
- The directions [100], [011], and [111] represent the directions along these axes.
- The Miller indices of a plane in a cubic structure are represented by three integers (hkl), where h, k, and l are the intercepts of the plane with the x, y, and z axes, respectively.

2. Determine the intercepts of the plane with the axes:
- The plane contains the direction [100], which means it intercepts the x-axis at 1.
- The plane contains the direction [011], which means it intercepts the y-axis at 1.
- The plane contains the direction [111], which means it intercepts the z-axis at 1.

3. Determine the Miller indices:
- The intercepts of the plane with the x, y, and z axes are 1, 1, and 1, respectively.
- To find the Miller indices, we take the reciprocals of the intercepts and multiply by a common factor to obtain the smallest set of integers.
- In this case, the reciprocals of 1, 1, and 1 are 1, 1, and 1, respectively.
- Multiplying by a common factor, we obtain the Miller indices (hkl) as (1, 1, 1).

4. Determine the correct option:
- Option 'a' represents the Miller indices (011), which is incorrect.
- Option 'b' represents the Miller indices (101), which is incorrect.
- Option 'c' represents the Miller indices (100), which is incorrect.
- Option 'd' represents the Miller indices (110), which is incorrect.
- Therefore, the correct option is 'a', which represents the Miller indices (111) as determined in step 3.

In conclusion, the Miller indices of the plane in the cubic structure that contains all the directions [100], [011], and [111] is represented by the Miller indices (111), which corresponds to option 'a'.