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

Six cards and six envelopes are numbered $1, 2, 3, 4, 5, 6$. Cards are to be placed in envelopes such that each envelope contains exactly one card,no card is placed in the envelope bearing the same number,and the card numbered $1$ is always placed in the envelope numbered $2$. The number of ways this can be done is:

$A$ person has three different bags and four different books. The number of ways, in which he can put these books in the bags so that no bag is empty, 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 $...........$.

If $4$ letters are placed randomly into $4$ envelopes,what is the probability that none of the letters are placed in their correct envelopes?

The number of arrangements of all digits of $12345$ such that at least $3$ digits will not come in their original positions is