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 number of arrangements of the letters of the word $BANANA$ in which two $N$s do not appear adjacently is

Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many ways can we place the balls so that no box remains empty?

If the different permutations of the word $EXAMINATION$ are listed as in a dictionary,how many items are there in this list before the first word starting with $E?$

The number of $4$-digit even numbers that can be formed using $0, 1, 2, 3, 4, 5, 6$ without repetition is

There are $10$ persons named $A, B, \dots, J$. We have the capacity to accommodate only $5$. In how many ways can we arrange them in a line if $A$ must be included and $G$ and $H$ must not be included in the team of $5$?