The number of circular permutations of $n$ different objects is

An eight-digit number divisible by $9$ is to be formed using digits from $0$ to $9$ without repeating the digits. The number of ways in which this can be done is: (in $(7!)$)

If $n$ is a factor of $72$,such that $xy = n$,then the number of ordered pairs $(x, y)$ is: (where $x, y \in N$)

In how many ways can $6$ letters be posted in $5$ letter boxes available in the locality?

In how many ways can five examination papers be arranged so that physics and chemistry papers never come together?

$A = \{ x_1, x_2, x_3, x_4 \}; \, B = \{ y_1, y_2, y_3, y_4 \}.$ $A$ function is defined from set $A$ to set $B.$ The number of one-one functions such that $f(x_i) \neq y_i$ for $i = 1, 2, 3, 4$ is equal to: