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:

Find $n$ if ${ }^{n} P_{4}=18 \cdot{ }^{n-1} P_{2}$.

In how many ways can $7$ men and $7$ women be seated around a round table such that no two women sit together?

Ten persons,among whom are $A, B$,and $C$,are to speak at a function. The number of ways in which they can speak if $A$ wants to speak before $B$ and $B$ wants to speak before $C$ is:

How many words can be made from the letters of the word $DELHI$,if $L$ comes in the middle in every word?

In a city,no two persons have an identical set of teeth,and there is no person without a tooth. Also,no person has more than $32$ teeth. If we disregard the shape and size of the teeth and consider only the presence or absence of a tooth at each of the $32$ positions,then the maximum population of the city is: