In how many ways can $mn$ letters be posted in $n$ letter-boxes?

In how many ways can a committee consisting of $5$ men and $6$ women be formed from $8$ men and $10$ women?

If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman,then the number of seating arrangements is

The number of ways in which $3$ children can distribute $10$ tickets out of $15$ consecutively numbered tickets among themselves such that they get consecutive blocks of $5, 3$ and $2$ tickets is:

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

In how many ways can $21$ books on Sanskrit and $19$ books on French be placed in a row on a shelf such that two books on French may not be together?