If the best and the worst paper never appear together,then six examination papers can be arranged in how many ways?

If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman,then the number of seating arrangements is

From $6$ different novels and $3$ different dictionaries,$4$ novels and $1$ dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :

$A$ customer forgets a $4$-digit code for an Automatic Teller Machine ($A$.$T$.$M$.) in a bank. However,he remembers that this code consists of digits $3, 5, 6$ and $9$. Find the largest possible number of trials necessary to obtain the correct code.

For a set of $5$ true-or-false questions,no student has written all the correct answers,and no $2$ students have given the same sequence of answers. What is the maximum number of students in the class,for this to be possible?

$A$ box contains $2$ white balls,$3$ black balls and $4$ red balls. In how many ways can $3$ balls be drawn from the box,if at least one black ball is to be included in the draw?