The number of words,which can be formed using all the letters of the word $\text{DAUGHTER}$,so that all the vowels never come together,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

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

Let $P$ be the set of seven-digit numbers with the sum of their digits equal to $11$. If the numbers in $P$ are formed by using the digits $1, 2,$ and $3$ only,then the number of elements in the set $P$ is:

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