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?

Let $n_1 < n_2 < n_3 < n_4 < n_5$ be positive integers such that $n_1+n_2+n_3+n_4+n_5=20$. Then the number of such distinct arrangements $(n_1, n_2, n_3, n_4, n_5)$ is

$A$ debate club consists of $6$ girls and $4$ boys. $A$ team of $4$ members is to be selected from this club,including the selection of a captain (from among these $4$ members) for the team. If the team has to include at most one boy,then the number of ways of selecting the team is

In how many different ways can three persons $A, B, C$ having $6, 7$ and $8$ one-rupee coins respectively,donate $₹ 10$ collectively?

For which value of $n \in N$,does $n!$ have $13$ trailing zeros?

The number of integers $n$ such that $100 \leq n \leq 999$ and $n$ contains at most two distinct digits is: