The number of ways of distributing $500$ dissimilar boxes equally among $50$ persons is:

Evaluate $\frac{n!}{r!(n-r)!}$ when $n=5$ and $r=2$.

$A$ question paper is divided into two parts,$A$ and $B$,each consisting of $5$ questions. If a candidate has to select $6$ questions in total,in how many ways can they do so if they must select at least $2$ questions from each part?

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

In how many ways can $5$ red and $4$ white balls be drawn from a bag containing $10$ red and $8$ white balls?

If set $A$ contains $8$ elements,then the number of subsets of $A$ which contain at least $6$ elements is