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 :

How many words,with or without meaning,can be formed from the letters of the word $MONDAY$,assuming that no letter is repeated,if all letters are used at a time?

Find $n$ if $^{n-1}P_{3} : ^{n}P_{4} = 1 : 9$.

The letters of the word $ARRANGE$ are used to form different words. All these words are arranged in dictionary order. What is the rank of the word $ARRANGE$ in the dictionary?

Eight chairs are numbered $1$ to $8$. Two women and three men wish to occupy one chair each. First,the women choose the chairs from amongst the chairs marked $1$ to $4$,and then the men select the chairs from amongst the remaining. The number of possible arrangements is

How many words,with or without meaning,each of $2$ vowels and $3$ consonants can be formed from the letters of the word $DAUGHTER$?