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

Mahesh has $6$ friends. In how many ways can he invite one or more friends for dinner?

The number of ways to distribute $25$ identical apples among $4$ boys,such that each boy receives at least $4$ apples,is

$A$ bag contains $5$ red marbles,$4$ black marbles,and $3$ white marbles. The number of ways in which $4$ marbles can be drawn so that at most $2$ of them are red is:

If the number of subsets with $8$ elements from the set $A=\{a_1, a_2, a_3, \ldots, a_n\}$,$n \geq 8$,is five times the number of such subsets containing $a_4$,then $n=$

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 $5$?