An examination has $3$ multiple-choice questions,and each question has $4$ options. If a student passes only if they answer all questions correctly,in how many ways can they fail?

The sum of the four-digit even numbers that can be formed with the digits $0, 3, 5, 4$ without repetition is:

The total number of $5$-digit numbers, formed by using the digits $1, 2, 3, 5, 6, 7$ without repetition, which are multiples of $6$, is

The number of four-letter words that can be formed using the letters of the word $BARRACK$ is

The number of all possible combinations of $4$ letters which are taken from the letters of the word $ACCOMMODATION$ is

All the arrangements,with or without meaning,of the word $FARMER$ are written excluding any word that has two $R$ appearing together. The arrangements are listed serially in the alphabetic order as in the English dictionary. Then the serial number of the word $FARMER$ in this list is .... .