Four notes of Rs. $100$ and one note each of Rs. $1$,Rs. $2$,Rs. $5$,Rs. $20$,and Rs. $50$ are to be distributed among $3$ children such that each child receives at least one note of Rs. $100$. In how many ways can this distribution be done?

In how many ways can $3$ letters be posted in $4$ letter boxes,if all the letters are not posted in the same letter box?

Five boys and five girls are writing an examination in a hall in which $5$ benches are arranged in a row and only two students are to be seated on every bench at either of its ends. If the seating arrangement is to be such that no two boys or no two girls sit together as neighbours (a student should not have a student of same gender either on left or right),then the total number of such arrangements is

Let $n = 1! + 4! + 7! + \ldots + 400!$. Then the ten's digit of $n$ is

The number of times the digit $3$ will be written when listing the integers from $1$ to $1000$ is

The number of four-digit numbers formed by using the digits $0, 2, 4, 5$ (without repetition) which are not divisible by $5$ is: