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

In how many ways can 5 balls be placed in 4 tins if any number of balls can be placed in any tin?