In how many ways can a pack of $52$ cards be divided into four equal groups?

The number of ways of dividing $15$ persons into $3$ groups containing $3, 5$ and $7$ persons such that two particular persons are not included in the $5$-person group 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

If there are $6$ letters and $6$ corresponding envelopes,in how many ways can all the letters be placed in the wrong envelopes?

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

In an examination,$5$ students have been allotted their seats as per their roll numbers. The number of ways,in which none of the students sits on the allotted seat,is $..........$.