Out of $8$ students in a classroom,$4$ of them are chosen and they are arranged around a table. If the remaining $4$ are arranged in a row,then the total number of arrangements that can be made with those $8$ students is

The smallest positive integer $n$,for which $n! < {\left( {\frac{{n + 1}}{2}} \right)^n}$ holds is

If four letters are chosen from the letters of the word $ASSIGNMENT$ and are arranged in all possible ways to form $4$-letter words (with or without meaning),then the total number of such words that can be formed is:

There are three sections in a question paper,each section containing $4$ questions. If a candidate has to answer exactly $5$ questions from this paper such that at least one question is answered from each section,then the number of ways in which a candidate can make the choice of questions is

The number of positive integers less than $10000$ which contain the digit $5$ at least once is

Let the digits $a, b, c$ be in $A.P.$ Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in $A.P.$ at least once. How many such numbers can be formed?