If $5$ letters are to be placed in $5$ addressed envelopes,then the probability that at least one letter is placed in the wrongly addressed envelope is

There are $n$ letters and $n$ addressed envelopes. The probability that all the letters are not kept in the right envelope is:

Eight persons are to be transported from city $A$ to city $B$ in three cars of different makes. If each car can accommodate at most three persons,then the number of ways,in which they can be transported,is $...........$.

There are $4$ balls of different colors and $4$ boxes of the same colors as the balls. In how many ways can $2$ balls be placed in the boxes such that they do not match their respective colors?

$150$ students took admission. In how many ways can they be divided into three equal sections $A, B,$ and $C$?

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