If the letters of the word $MOTHER$ are permuted and all the words so formed (with or without meaning) are listed as in a dictionary,then the position of the word $MOTHER$ is

How many $8$-digit numbers can be formed such that all digits are distinct?

Words of length $10$ are formed using the letters $A, B, C, D, E, F, G, H, I, J$. Let $x$ be the number of such words where no letter is repeated,and let $y$ be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then,$\frac{y}{9x} =$

How many numbers can be formed using the digits $1, 2, 3, 4$ if repetition of digits is not allowed?

The number of ways in which all the letters of the word $COMBINATION$ can be arranged so that the vowels always come together is:

$S_1, S_2, \ldots, S_{10}$ are the speakers in a conference. If $S_1$ addresses only after $S_2$,then the number of ways the speakers address is