If a polygon of $$n$$ sides has 560 diagonals, then $$n=$$

A person writes letters to 6 friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes? Notation $$D_n=n!\left(\sum_\limits{i=0}^n \frac{(-1)^i}{i!}\right)$$

The value of $${ }^6 P_4+4 \cdot{ }^6 P_3$$ is

The number of ways in which 3 boys and 2 girls can sit on a bench so that no two boys are adjacent is