Two queens, placed at random on a chess board, the probability that they are not in clashing position is p then $36P-19=$(queens can move in row, column and diagonally and [.] is GIF)

The queens will be facing each other in case both are placed on the same column, the same row or the same diagonal of the chess board. There are eight rows, eight columns, two principal diagonals and four sets each containing  lines of 7,6,5,4,3,2,1 square. Hence the probability of the queens taking on each other is

$P\left(\overline{A}\right)=\frac{{18}^8{c}_2+4{(}^7{c}_2{+}^6{c}_2{+}^5{c}_2{+}^4{c}_2{+}^3{c}_2{+}^2{c}_2)}{{ }^{64}{c}_2}$

$=\frac{18\times 8\times 7+4[7\times 6+6\times 5+5\times 4+4\times 3+3\times 2+2\times 1]}{64\times 63}$

$=\frac{18\times 7+[7\times 3+3\times 5+5\times 2+2\times 3+3\times 1]}{64\times 63}=\frac{18\times 7+[7\times 3+3\times 7+14]}{8\times 63}$

$\frac{18+6+2}{8\times 9}=\frac{26}{72}=\frac{13}{36}$

Hence the probability that the two queen to not take on each other is P(A)=1 $-\frac{13}{36}=\frac{23}{36}$