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

The number of rectangles that can be obtained by joining four of $12$ vertices of a $12$-sided regular polygon is:

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

How many numbers greater than $24000$ can be formed by using the digits $1, 2, 3, 4, 5$ when no digit is repeated?

The number of ways in which an examiner can assign $30$ marks to $8$ questions,awarding not less than $2$ marks to any question is

There are $6$ candidates for $3$ posts. In how many ways can the posts be filled?