$P, Q, R$ and $S$ have to give lectures to an audience. The organiser can arrange the order of their presentation in ............. ways.

Total number of four-digit odd numbers that can be formed using $0, 1, 2, 3, 5, 7$ (repetition allowed) are

How many five-digit numbers can be formed using the digits $2, 0, 4, 3, 8$ if repetition of digits is not allowed?

The number of ways in which $5$ boys and $3$ girls can be seated on a round table if a particular boy $B_1$ and a particular girl $G_1$ never sit adjacent to each other,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?

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