In how many ways can Rs. $16$ be divided among $4$ persons if none of them gets less than Rs. $3$?

The number of ways of distributing $500$ dissimilar boxes equally among $50$ persons is:

In how many ways can $11$ identical pencils be distributed among $6$ children such that each child receives at least one pencil?

If $^{43}C_{r-6} = ^{43}C_{3r+1}$,then the value of $r$ is

What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these do the four cards belong to four different suits?

Consider three boxes,each containing $10$ balls labelled $1, 2, \dots, 10$. Suppose one ball is randomly drawn from each of the boxes. Denote by $n_i$ the label of the ball drawn from the $i^{th}$ box,$(i = 1, 2, 3)$. Then,the number of ways in which the balls can be chosen such that $n_1 < n_2 < n_3$ is: