In how many ways can a cricket team of $11$ players be selected out of $16$ players if $1$ particular player is to be excluded?

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?

If $x, y$ and $r$ are positive integers, then $^x{C_r} + ^x{C_{r-1}} \cdot ^y{C_1} + ^x{C_{r-2}} \cdot ^y{C_2} + \dots + ^y{C_r} = $

Out of $7$ consonants and $4$ vowels,how many words of $3$ consonants and $2$ vowels can be formed?

In how many ways can $6$ persons be selected from $4$ officers and $8$ constables,if at least one officer is to be included?

The number of different $6$-digit numbers that are divisible by $10$,which can be formed using the digits $1, 2, 7, 0, 9, 5$?