The number of ways in which $3$ men and $3$ women can be arranged in a row of $6$ seats,such that the first and last seats must be filled by men is

The number of $9$-digit numbers that can be formed using all the digits of the number $123412341$ such that the even digits occupy only even places 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

How many words can be formed using the letters of the word $BHARAT$ such that $B$ and $H$ never come together?

The letters of the word $COCHIN$ are permuted and all permutations are arranged in alphabetical order as in an English dictionary. The number of words that appear before the word $COCHIN$ is

Evaluate $4! - 3!$