$P, Q, R$ and $S$ have to give lectures to an audience. The organiser can arrange the order of their presentation in ............. ways.

All the letters of the word $PUBLIC$ are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word $PUBLIC$ is

The letters of the word $MODESTY$ are written in all possible orders and these words are written out as in a dictionary. Then,the rank of the word $MODESTY$ is:

There are $11$ distinct books on a shelf,consisting of $5$ Mathematics,$4$ Physics,and $2$ Chemistry books. In how many ways can they be arranged such that books of the same subject are always kept together?

If $3$ books on Physics,$2$ books on Chemistry,and $4$ books on Mathematics are to be arranged on a shelf so that all the Physics books are together and all the Mathematics books are together,then the number of such arrangements is

How many words can be formed using the letters of the word $ALLAHABAD$?