Probability

A chessboard consists of 8x8 squares forming a square. A rook is unthreatened if there is no other rook in the row and column in which it stands. What is the probability that when 8 rooks are placed on a chessboard, none of them threaten each other (they stand in different rows and different columns)

Correct answer:

p =  42.1488 %

Step-by-step explanation:

$$\begin{gathered} n=8!=40320 \\ p=100\cdot \frac{8\cdot 8+7\cdot 7+6\cdot 6+5\cdot 5+4\cdot 4+3\cdot 3+2\cdot 2+1\cdot 1}{64+63+62+61+60+59+58+57}=\frac{5100}{121}\%=42.1488\% \end{gathered}$$

Try another example