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:

Each of the $10$ letters $A, H, I, M, O, T, U, V, W$ and $X$ appears the same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many three-letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?

The number of ways in which $3$ boys and $4$ girls can be seated around a circular table if no two boys sit together is:

Given six line segments of lengths $2, 3, 4, 5, 6, 7$ units,the number of triangles that can be formed by these lines is

If $(n+1)! = 6[(n-1)!]$,find $n$.

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?