X is the number of geometrical isomers exhibited by $$[Pt(NH_{3})(H_{2}O)BrCl]$$.
Y is the number of optically inactive isomer(s) exhibited by $$[CrCl_{2}(ox)_{2}]^{3-}$$
z is the number of geometrical isomers exhibited by $$[Co(NH_{3})_{3}(NO_{2})_{3}]$$.
The value of X + Y + Z is________.

We need to find X + Y + Z where X, Y, and Z relate to different coordination compound isomers.

We begin by finding X, the number of geometrical isomers of $$[Pt(NH_3)(H_2O)BrCl]$$. This is a square planar complex (Pt(II) with d$$^8$$ configuration) with four different monodentate ligands: $$NH_3$$, $$H_2O$$, $$Br^-$$, and $$Cl^-$$.

A square planar complex $$[MABCD]$$ with 4 different ligands has 3 geometrical isomers. These correspond to the three ways of choosing which pair of ligands are trans to each other:

1. $$NH_3$$ trans to $$H_2O$$, $$Br$$ trans to $$Cl$$

2. $$NH_3$$ trans to $$Br$$, $$H_2O$$ trans to $$Cl$$

3. $$NH_3$$ trans to $$Cl$$, $$H_2O$$ trans to $$Br$$

Therefore, X = 3.

Next, to find Y, we consider the optically inactive isomers of $$[CrCl_2(ox)_2]^{3-}$$, which is an octahedral complex with 2 chloride ions and 2 oxalate (bidentate) ligands. This complex shows two geometrical isomers:

- cis isomer: The two Cl atoms are adjacent. This isomer lacks a plane of symmetry and exists as a pair of non-superimposable mirror images (enantiomers). The cis isomer is optically active.

- trans isomer: The two Cl atoms are opposite to each other. This isomer has a plane of symmetry and is optically inactive.

Therefore, Y = 1 (only the trans isomer is optically inactive).

For Z, we examine the geometrical isomers of $$[Co(NH_3)_3(NO_2)_3]$$, an octahedral complex of the type $$[Ma_3b_3]$$. Such complexes exhibit two geometrical isomers:

- fac (facial): Three identical ligands occupy one face of the octahedron.

- mer (meridional): Three identical ligands occupy a meridian (one in the centre with two others at opposite ends).

Therefore, Z = 2.

Combining these results gives $$X + Y + Z = 3 + 1 + 2 = 6$$.

The answer is 6.