In how many different ways can the letters of the word '$BANKING$' be arranged?

There are $6$ multiple choice questions in an examination. How many sequences of answers are possible,if the first $2$ questions have $3$ choices each,the next $2$ have $4$ choices each,and the last $2$ have $5$ choices each?

On the sides $AB, BC, CA$ of a $\Delta ABC$,$3, 4, 5$ distinct points (excluding vertices $A, B, C$) are respectively chosen. The number of triangles that can be constructed using these chosen points as vertices are:

There are $6$ men and $8$ women in a club. $A$ committee of $5$ people has to be formed. What will be the number of ways to select $5$ people if $2$ men and $3$ women are selected?

From among the $36$ teachers in a school,one principal and one vice-principal are to be appointed. In how many ways can this be done?

The number of permutations of $n$ things taken $r$ at a time,when $p$ things are always included,is