In how many different ways can the letters of the word '$PRAISE$' be arranged?

$12$ persons are to be arranged at a round table. If two particular persons among them are not to be side by side,the total number of arrangements is

In how many ways can a girl and a boy be selected from a group of $15$ boys and $8$ girls?

Two packs of $52$ cards are shuffled together. The number of ways in which a man can be dealt $26$ cards so that he does not get two cards of the same suit and same denomination 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 ways of choosing $10$ objects out of $31$ objects,of which $10$ are identical and the remaining $21$ are distinct,is