How many numbers of five digits can be formed with the digits $0, 1, 2, 3, 5$ and $6$?

Let $n$ be the number of different $5$-digit numbers,divisible by $4$,formed with the digits $1, 2, 3, 4, 5,$ and $6$,such that no digit is repeated in the numbers. What is the value of $n$?

$4$ books,$1$ each in Chemistry,Physics,Biology,and Mathematics,are to be arranged on a shelf. In how many ways can this be done?

Consider a class of $5$ girls and $7$ boys. The number of different teams consisting of $2$ girls and $3$ boys that can be formed from this class,if there are two specific boys $A$ and $B$ who refuse to be members of the same team,is

In how many ways can a committee consisting of one or more members be formed out of $12$ members of the Municipal Corporation?

How many numbers of four digits can be formed with the digits $1, 2, 3, 4$ and $5$?