In an examination there are three multiple choice questions and each question has $4 $ choices. Number of ways in which a student can fail to get all answers correct, is
$11$
$12$
$27$
$63$
A set contains $2n + 1$ elements. The number of subsets of this set containing more than $n$ elements is equal to
Determine the number of $5 -$ card combinations out of a deck of $52$ cards if each selection of $5$ cards has exactly one king.
A person wants to climb a $n-$ step staircase using one step or two steps. Let $C_n$ denotes the number of ways of climbing the $n-$ step staircase. Then $C_{18} + C_{19}$ equals
The number of ways in which $10$ persons can go in two boats so that there may be $5 $ on each boat, supposing that two particular persons will not go in the same boat is
If $^8{C_r}{ = ^8}{C_{r + 2}}$, then the value of $^r{C_2}$ is