If $C(n, 8) = C(n, 6)$,find $C(n, 2)$.

If $^{20}C_{n+2} = ^nC_{16}$,then the value of $n$ is

How many $2$-digit numbers are there with distinct digits?

$A$ person is permitted to select at least one and at most $n$ coins from a collection of $(2n + 1)$ distinct coins. If the total number of ways in which he can select coins is $255$,then $n$ equals

Total number of $6$-digit numbers in which only and all the five digits $1, 3, 5, 7,$ and $9$ appear,is

Out of $18$ points in a plane,no three are in the same straight line except five points which are collinear. The number of $(i)$ straight lines,$(ii)$ triangles which can be formed by joining them is