The letters of the word $OUGHT$ are written in all possible ways and these words are arranged as in a dictionary,in a series. Then the serial number of the word $TOUGH$ is :

There are $9$ chairs in a room on which $6$ persons are to be seated. Out of these,one person is a guest who must occupy one specific chair. In how many ways can they sit?

Ten chairs are numbered as $1$ to $10$. Three women and two men wish to occupy one chair each. First,the women choose the chairs marked $1$ to $6$,then the men choose the chairs from the remaining. The number of possible ways is

How many arrangements can be made with $5$ boys and $5$ girls in a row such that boys and girls alternate?

How many $3$-digit even numbers can be formed using the digits $1, 2, 3, 4, 6, 7$,if no digit is repeated?

The number of three-digit even numbers,formed by the digits $0, 1, 3, 4, 6, 7$ if the repetition of digits is not allowed,is .... .