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

$A$ student is allowed to select at most $n$ books from a collection of $(2n+1)$ books. If the total number of ways in which one can select at least one book is $255$,then the value of $n$ is

The domain of the function $f(x) = {}^{(10-x)}C_{(x-6)}$ is...

There are $15$ persons in a party and each person shakes hands with every other person exactly once. The total number of handshakes is:

In how many ways can $11$ identical pencils be distributed among $6$ children such that each child receives at least one pencil?

If $\binom{n-1}{4}$,$\binom{n-1}{5}$,and $\binom{n-1}{6}$ are in arithmetic progression,find $n$.