If $33!$ is divisible by $2^n$,where $n \in N$,then the sum of all possible values of $n$ is:

If ${ }^{18} C_{r}={ }^{18} C_{r+2}$,find ${ }^{r} C_{5}$.

$4$ books,$1$ each in Chemistry,Physics,Biology,and Mathematics,are to be arranged on a shelf. In how many ways can this be done?

If $12 \cdot {}^{n}C_{2} = {}^{2n}C_{3}$,find $n$.

The number of diagonals in a polygon of $m$ sides is

Let $n > 2$ be an integer. Suppose that there are $n$ Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track. Further,each pair of nearest stations is connected by a blue line,whereas all remaining pairs of stations are connected by a red line. If the number of red lines is $99$ times the number of blue lines,then the value of $n$ is