If $^{{n^2} - n}{C_2}{ = ^{{n^2} - n}}{C_{10}}$, then $n = $
$12$
$4$ only
$- 3$ only
$4$ or $- 3$
$\sum \limits_{ k =0}^6{ }^{51- k } C _3$ is equal to
Out of $6$ books, in how many ways can a set of one or more books be chosen
In a city no two persons have identical set of teeth and there is no person without a tooth. Also no person has more than $32$ teeth. If we disregard the shape and size of tooth and consider only the positioning of the teeth, then the maximum population of the city is
The number of seven digit positive integers formed using the digits $1,2,3$ and $4$ only and sum of the digits equal to $12$ is $...........$.
The total number of different combinations of one or more letters which can be made from the letters of the word ‘$MISSISSIPPI$’ is