If the best and the worst paper never appear together,then in how many ways can $6$ examination papers be arranged?

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

The number of all four-digit numbers which begin with $4$ and end with either $0$ or $5$ is:

The number of all $8$-digit odd numbers is

The number of arrangements of the word $KANGAROO$ in which $A$'s do not appear together is

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