If $\binom{15}{3r} = \binom{15}{r+3}$,then $r = \dots$

There are $10$ persons named $A, B, \dots, J$. We have the capacity to accommodate only $5$. In how many ways can we arrange them in a line if $A$ must be included,and $G$ and $H$ must not be included in the team of $5$?

How many words of $4$ distinct letters can be formed using the letters of the word $DHOLPUR$ such that $L$ and $P$ are always included?

In how many ways can $16$ rupees be divided among $4$ persons such that no person receives less than $3$ rupees?

The number of ways in which an examiner can assign $30$ marks to $8$ questions,giving not less than $2$ marks to any question,is

$A$ father with $8$ children takes $3$ children to the zoo at a time. If he can go more than once without taking the same $3$ children together,in how many ways can the father go to the zoo?