The possible number of stereoismers for the formula `[Ma_(2)bcde]^(pmn)`.

Answer

To determine the possible number of stereoisomers for the coordination compound \([Ma_2bcde]^{pmn}\), we will follow these steps:

### Step 1: Identify the Coordination Number and Geometry
The given complex has the formula \([Ma_2bcde]^{pmn}\). Here, 'M' represents the metal center, and 'a', 'b', 'c', 'd', and 'e' are the ligands. The coordination number is determined by the number of donor atoms from the ligands that are coordinated to the metal.

**Hint:** The coordination number is equal to the number of ligands attached to the metal center.

### Step 2: Determine the Types of Isomers
In coordination chemistry, stereoisomers can be classified into two main types: geometrical isomers and optical isomers.

- **Geometrical Isomers:** These arise from different spatial arrangements of ligands around the metal center.
- **Optical Isomers:** These arise when the arrangement of ligands creates non-superimposable mirror images.

**Hint:** Consider how the arrangement of ligands can differ in space to form different isomers.

### Step 3: Calculate Geometrical Isomers
For the given complex \([Ma_2bcde]^{pmn}\), we can deduce that it has two identical ligands 'a' and four different ligands 'b', 'c', 'd', and 'e'. The geometrical isomers can be calculated based on the arrangement of these ligands.

- The presence of two identical ligands typically allows for several arrangements. For example, if the ligands 'a' are adjacent or opposite each other, this will lead to different geometrical isomers.

**Hint:** Use combinatorial logic to determine how many unique arrangements can be formed with the given ligands.

### Step 4: Calculate Optical Isomers
Once the geometrical isomers are determined, we can then analyze how many of these isomers are optically active. Optical isomers are determined by the presence of chiral centers in the molecule.

- A chiral center is typically created when a ligand arrangement results in non-superimposable mirror images.

**Hint:** Check each geometrical isomer to see if it has a plane of symmetry. If it does not, it is likely optically active.

### Step 5: Sum Up the Total Stereoisomers
Finally, the total number of stereoisomers is the sum of the geometrical and optical isomers.

- In this case, the video transcript indicates that there are 9 geometrical isomers and 15 optical isomers, leading to a total of 15 stereoisomers.

**Hint:** Ensure to count both types of isomers correctly before summing them up.

### Conclusion
The total number of possible stereoisomers for the coordination compound \([Ma_2bcde]^{pmn}\) is **15**.