Find the number of ways in which 2 identical kings can be placed on an n x m chessboard so that the kings are not in adjacent squares.

first king can be placed in n*m places

1)one king at corner ,other king will be at = 4  *  [(n*m)-4] places    = 4mn-16

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                                                     4 corners   [m*n places - 4 places around] 

2)one king at edge, other will be at= [2(n-2)+2(m-2)]  *  (n*m-5) = 2mn²-10n+2m²n-10m-8mn+40

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                                       number of box at edge      m*n places except 5 places around

3)one king at free from corners and edges, other will be at

                      = [(n-2)*(m-2)]     *        (n*m-8)      =   n²m²-2n²m-2nm²-4nm+16n+16m-32

                                ↑                                 ↑  

  number of boxes away from ends           n*m places except 8 places around

sum of all probablities will be= (nm-4)²+6(m+n-4)

sorry this isnt the ans.

then tell me the right solution

as it was disapproved