Which of the following order is representing increasing order of geometrical isomers of given complexes ?

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${[M (AA) b_{2} c_{2}]}^{n \pm}; {[{Ma}_{2} b_{2} c_{2}]}^{n \pm}; {[{Ma}_{3} bcd]}^{n \pm}; {[{Ma}_{2} bcde]}^{n \pm}$

${[M (AA) b_{2} c_{2}]}^{n \pm}; {[{Ma}_{3} bcd]}^{n \pm}; {[{Ma}_{2} b_{2} c_{2}]}^{n \pm}; {[{Ma}_{2} bcde]}^{n \pm}$

${[{Ma}_{3} bcd]}^{n \pm}; {[{Ma}_{2} b_{2} c_{2}]}^{n \pm}; {[M (AA) b_{2} c_{2}]}^{n \pm}; {[{Ma}_{2} bcde]}^{n \pm}$

${[{Ma}_{2} b_{2} c_{2}]}^{n \pm}; {[M (AA) b_{2} c_{2}]}^{n \pm}; {[{Ma}_{3} bcd]}^{n \pm}; {[{Ma}_{2} bcde]}^{n \pm}$

answer is B.

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Detailed Solution

$\begin{array}{l} {[M (AA) b_{2} c_{2}]}^{n \pm}; Total GI = 3 [1 cis + 2 trans] \\ {[{Ma}_{3} bcd]}^{n \pm}; Total GI = 4 [1 cis + 3 trans] \\ {[{Ma}_{2} b_{2} c_{2}]}^{n \pm}; Total GI = 5 [1 cis + 4 trans] \\ {[{Ma}_{2} bcde]}^{n \pm}; Total GI = 9 [6 cis + 3 trans] \end{array}$