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

An eight-digit number divisible by $9$ is to be formed using digits from $0$ to $9$ without repeating the digits. The number of ways in which this can be done is: (in $(7!)$)

The number of different words that can be formed using all the letters of the word $APPLICATION$ such that no two vowels come together is -

$^{80}C_{40}$ is not divisible by -

The number of four-lettered words that can be formed from the letters of the word $MAYANK$ such that both $A$'s are included but never together,is equal to:

Five-digit numbers are formed using the digits $1, 2, 3, 5, 7$ with repetitions and are written in descending order with serial numbers. For example,the number $77777$ has serial number $1$. Then the serial number of $35337$ is $.........$.