The remainder obtained when $1! + 2! + 95!$ is divided by $15$ is

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

$^n{P_r} \div ^n{C_r} = $

The number of triplets $(x, y, z)$,where $x, y, z$ are distinct non-negative integers satisfying $x+y+z=15$,is

In an examination,the maximum marks for each of three subjects is $n$ and that for the fourth subject is $2n$. The number of ways in which a candidate can get $3n$ marks is

From a collection of $20$ consecutive natural numbers,four are selected such that they are not consecutive. The number of such selections is