In an examination hall,there are $mn$ chairs arranged in $m$ rows and $n$ columns. The number of ways in which $m$ students can be seated such that no row is vacant is:

Seven scientists $S_1, S_2, \ldots, S_7$ are invited to deliver one lecture each in a conference. The number of ways all the seven lectures can be arranged such that the lecture of $S_1$ is prior to that of $S_3$ and the lecture of $S_3$ is prior to that of $S_7$ is

In how many ways can the letters of the word $EAMCET$ be arranged such that no two vowels are together?

How many words can be made from the letters of the word $DELHI$,if $L$ comes in the middle in every word?

How many numbers greater than $10$ lakh can be formed using the digits $2, 3, 0, 3, 4, 2, 3$?

Out of $10$ persons,$A, B$,and $C$ are to speak at a function. If $A$ wants to speak before $B$ and $B$ wants to speak before $C$,in how many ways can they speak?