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

The total number of integral solutions of the equation $xyz = 24$ is

Let $n$ be the number of ways in which $5$ boys and $5$ girls can stand in a queue such that all the girls stand consecutively. Let $m$ be the number of ways in which $5$ boys and $5$ girls can stand in a queue such that exactly four girls stand consecutively. Then the value of $\frac{m}{n}$ is

The remainder obtained when $1! + 2! + 3! + \dots + 11!$ is divided by $12$ is

$A$ test containing $3$ objective-type questions is conducted in a class. Each question has $4$ options and only one option is the correct answer. No two students of the class have answered identically,and no student has written all correct answers. If every student has attempted all the questions,then the maximum possible number of students who have written the test is:

In how many ways can $3$ letters be posted in $4$ letter boxes,if all the letters are not posted in the same letter box?