If $n$ and $r$ are two positive integers such that $n \ge r,$ then $^nC_{r-1} + ^nC_r = $

$A$ student has to answer $10$ questions,choosing at least $4$ from each of the parts $A$ and $B$. If there are $6$ questions in part $A$ and $7$ in part $B$,then the number of ways the student can choose $10$ questions is:

$A$ committee of $7$ members is to be formed from $6$ boys and $4$ girls such that the number of boys is greater than the number of girls. In how many ways can this be done?

The number of ways in which $17$ apples can be distributed among $4$ guests such that each guest gets at least $3$ apples is

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

In an election,there are $8$ candidates,out of which $5$ are to be chosen. If a voter may vote for any number of candidates but not greater than the number to be chosen,then in how many ways can a voter vote?