A test containing 3 objective type of 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 answer. If every students has attempted all the questions, then the maximum possible number of students who has written the test is

The number of numbers lying between 1000 and 10000 such that every number contains the digit 3 and 7 only once without repetition is

The number of ways in which 17 apples can be distributed among four guests such that each guest gets at least 3 apples is .

If a polygon of $n$ sides has 275 diagonals, then $n$ is