5. On the cells of a chessboard of size $8 \times 8$, 6 identical pieces are randomly placed. Find the probability that five of them will be located either on the same row, or on the same column, or on one of the two main diagonals.
Answer: $P(A)=\frac{18 \cdot\left(C_{8}^{5} \cdot C_{56}^{1}+C_{8}^{6}\right)}{C_{64}^{6}}=\frac{28 \cdot 113 \cdot 18}{59 \cdot 61 \cdot 62 \cdot 21 \cdot 16}=\frac{339}{446276} \approx 0.00076$.