If $^{2017}C_0 + ^{2017}C_1 + ^{2017}C_2 + ...... + ^{2017}C_{1008} = \lambda^2$ where $\lambda > 0$,then the remainder when $\lambda$ is divided by $33$ is:

There are three bags $B_1$,$B_2$,and $B_3$ containing $2$ Red and $3$ White,$5$ Red and $5$ White,and $3$ Red and $2$ White balls respectively. $A$ ball is drawn from bag $B_1$ and placed in bag $B_2$,then a ball is drawn from bag $B_2$ and placed in bag $B_3$,then a ball is drawn from bag $B_3$. The number of ways in which this process can be completed,if the same colour balls are used in the first and second transfers (Assume all balls to be different) is

The number of triangles that can be formed by choosing the vertices from a set of $12$ points,seven of which lie on the same straight line,is

The number of ways in which we can select three numbers from $1$ to $30$ so as to exclude every selection of all even numbers is

How many numbers greater than $24000$ can be formed by using the digits $1, 2, 3, 4, 5$ when no digit is repeated?

In how many ways can a cricket team of $11$ players be selected out of $16$ players if $2$ particular players are to be included and $1$ particular player is to be rejected?