$10$ men and $6$ women are to be seated in a row so that no two women sit together. The number of ways they can be seated is:

How many numbers greater than $100$ and divisible by $5$ can be made from the digits $3, 4, 5, 6$,if no digit is repeated?

How many $3$-digit numbers can be formed by using the digits $1$ to $9$ if no digit is repeated?

If all the words (with or without meaning) having five letters,formed using the letters of the word $SMALL$ and arranged as in a dictionary,then the position of the word $SMALL$ is:

Words of length $10$ are formed using the letters $A, B, C, D, E, F, G, H, I, J$. Let $x$ be the number of such words where no letter is repeated,and let $y$ be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then,$\frac{y}{9x} =$

If all the digits in the number $53426$ are permuted in all possible ways and are arranged in decreasing order,then the number having rank $89$ is: