If there are $4$ letters and $4$ envelopes,in how many ways can all the letters be placed in the wrong envelopes?

The number of ways of distributing $3$ dozen fruits (no two fruits are identical) to $9$ persons such that each gets the same number of fruits is

If there are $5$ letters written to $5$ different people and $5$ envelopes addressed to them,then the number of ways in which these letters can be arranged so that no letter goes into its corresponding envelope is

Five letters are placed at random in five addressed envelopes. The probability that all the letters are not dispatched in the respective right envelopes is

There are four balls of different colours and four boxes of colours same as those of the balls. The number of ways in which the balls,one in each box,could be placed such that a ball does not go to the box of its own colour is

There are $n$ different objects $1, 2, 3, \dots, n$ distributed at random in $n$ places marked $1, 2, 3, \dots, n$. The probability that at least three of the objects occupy places corresponding to their number is