There are $9$ chairs in a room on which $6$ persons are to be seated. Out of these $6$ persons,one is a guest who must sit on one specific chair. In how many ways can they be seated?

The principal wants to arrange $5$ students on the platform such that the boy $SUNIL$ occupies the second position and such that the girl $GITA$ is always adjacent to the girl $NITA$. How many such arrangements are possible?

The number of nine-digit even natural numbers formed using only the digits $0$ and $1$, such that no two consecutive digits are $0$, is:

$A$ teacher of a class wants to set $1$ question from each of $2$ exercises in a book. If there are $15$ and $12$ questions in the $2$ exercises respectively,then in how many ways can the $2$ questions be selected?

How many $4$-digit numbers are there with distinct digits?

In an examination,there are three multiple-choice questions,and each question has $4$ choices. The number of ways in which a student can fail to get all answers correct is: