There are $6$ periods in each working day of a school. The number of ways one can arrange $5$ subjects such that each is allowed at least one period is:

There are $9$ chairs in a room,and $6$ people are to be seated. One of these chairs is a special chair reserved for a special guest. In how many ways can these people be seated?

The number of odd numbers greater than $6,00,000$ that can be formed by using the digits $3, 6, 7, 8, 9, 0$ without repetition is

How many even numbers of $3$ different digits can be formed from the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ (repetition is not allowed)?

Three children,each accompanied by a guardian,seek admission in a school. The principal wants to interview all the $6$ persons one after the other subject to the condition that no child is interviewed before its guardian. In how many ways can this be done?

The number of $7$ digit numbers which can be formed using the digits $1, 2, 3, 2, 3, 3, 4$ is