$9$ balls are to be placed in $9$ boxes. $3$ boxes are so small that they cannot hold $5$ balls. In how many ways can one ball be placed in each box?

$A$ 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 invited,is:

The total number of two-digit numbers $n$ such that $3^{n} + 7^{n}$ is a multiple of $10$ is ..... .

The number of $4$-digit integers in the closed interval $[2022, 4482]$ formed by using the digits $0, 2, 3, 4, 6, 7$ is:

What is the remainder when $1! + 2! + 3! + \dots + 200!$ is divided by $14$?

The number of $3$-digit odd numbers divisible by $3$ that can be formed using the digits $1, 2, 3, 4, 5, 6$ when repetition is not allowed is: