If $\binom{189}{35} + \binom{189}{x} = \binom{190}{x}$,then $x = \dots$

If $\binom{2n}{3} : \binom{n}{2} = 44 : 3$ and $\binom{n}{r} = 15$,then $r = \dots$

The number of ways to select one or more books from $6$ books is:

If the number of $5$-element subsets of the set $A = \{a_1, a_2, \dots, a_{20}\}$ containing $20$ distinct elements is $k$ times the number of $5$-element subsets containing the element $a_4$,then what is the value of $k$?

From a group of $10$ men and $8$ women,the number of ways of forming a committee of $8$ members with not more than $5$ men and not less than $5$ women is

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?