Consider the set $A = \{1, 2, 3, \ldots, 30\}$. The number of ways in which one can choose three distinct numbers from $A$ such that the product of the chosen numbers is divisible by $9$ is:

The number of triplets $(x, y, z)$,where $x, y, z$ are distinct non-negative integers satisfying $x+y+z=15$,is

If $_nP_r = 30240$ and $\binom{n}{r} = 252$,then $(n, r) = \dots$

The units digit of $\sum\limits_{1 < p < 100} {p! - \sum\limits_{n = 1}^{50} {(2n)!} }$ is:

The number of ordered pairs $(x, y)$ of integers such that their product $xy$ is a positive integer less than $100$ is:

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?