Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
An octahedral complex has one symmetric ring (AA) and four monodentate ligands, two of kind B and two of kind C. It has the type . Find the number of geometrical isomers and the number of stereoisomers.
Write the complex as trans pairs. The same pairs mean the same geometrical isomer. For monodentate ligands a mirror plane exists if one pair is two identical ligands or two pairs are the same. A ring takes two cis corners. Stereoisomers = geometrical isomers + chiral isomers.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Treat the two ring ends as two A ends on different axes. Each end is trans to one of the four single ligands. The last two ligands form the third pair.
Step 1. The sets. The ends can be trans to B and B, with C and C as the third pair. They can be trans to C and C, with B and B as the third pair. Or one end is trans to B and the other to C, with B and C as the third pair. That is 3 geometrical isomers.
Step 2. Mirror planes. In the first two sets the third pair is two identical ligands, so the ring plane is a mirror plane. These two are achiral. In the third set the three pairs are and there is no plane. It exists as two mirror images.
Step 3. Total. stereoisomers.
Check. Run the program with the word "AA B B C C" and compare.
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