If the domain and range of $f(x) = ^{9-x}C_{x-1}$ contain $m$ and $n$ elements respectively,then:

In an election,$3$ members are to be elected from $6$ candidates. $A$ voter can cast their vote for any number of candidates but not more than the number of candidates to be elected. In how many ways can a voter cast their vote?

If $^nC_3 + ^nC_4 > ^{n+1}C_3$,then

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:

If $n$ objects are arranged in a row,then the number of ways of selecting three of these objects such that no two of them are next to each other is:

The total number of all those $3$-digit numbers in which the sum of all the digits in each of them is $10$,is