$A$ student is required to answer $10$ questions out of $13$ in an examination,such that he must choose at least $4$ questions from the first $5$ questions. How many ways can he make the selection?

$\binom{n}{r+1} + 2\binom{n}{r} + \binom{n}{r-1} = \dots$

$\binom{n}{r} \div \binom{n}{n-1} = \dots$

In how many ways can $35$ apples be distributed among $3$ boys such that each boy can have any number of apples?

In an election,a voter can vote for any number of candidates but not more than the number of candidates to be elected. There are $10$ candidates and $4$ are to be elected. If a voter must vote for at least one candidate,in how many ways can they vote?

$A$ bag contains $5$ black and $6$ red balls. Determine the number of ways in which $2$ black and $3$ red balls can be selected.