The sum of all numbers formed by using all the digits $3, 1, 7, 9$ exactly once is:

If the digits are not allowed to repeat in any number formed by using the digits $0, 2, 4, 6, 8$,then the number of all numbers greater than $10,000$ is equal to $....$

Find the number of different $8$-letter arrangements that can be made from the letters of the word $DAUGHTER$ such that all vowels do not occur together.

We are to form different words with the letters of the word $INTEGER$. Let $m_1$ be the number of words in which $I$ and $N$ are never together and $m_2$ be the number of words which begin with $I$ and end with $R$,then $m_1/m_2$ is equal to

The number of arrangements of the letters of the word $MANAMA$ in which two $M$'s do not appear adjacent is

$A$ three-digit number $n$ is such that the last two digits are equal and differ from the first digit. The number of such $n$'s is: