The number of $7$-digit numbers which can be formed using the digits $1, 2, 3, 2, 3, 3, 4$ is:

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

The number of ways in which $6$ distinct rings can be worn on the $4$ fingers of one hand is:

$A$ man $X$ has $7$ friends,$4$ of them are ladies and $3$ are men. His wife $Y$ also has $7$ friends,$3$ of them are ladies and $4$ are men. Assume $X$ and $Y$ have no common friends. The total number of ways in which $X$ and $Y$ together can throw a party inviting $3$ ladies and $3$ men,such that $3$ friends of each of $X$ and $Y$ are in this party,is:

$A$ set contains $(2n + 1)$ elements. The number of subsets of the set which contain at most $n$ elements is:

How many $3$-digit numbers can be formed by using the digits $0, 2, 3, 6, 8$ when the digits may be repeated any number of times?