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 $...........$.
$412$
$411$
$413$
$414$
$^n{C_r}{ + ^{n - 1}}{C_r} + ......{ + ^r}{C_r}$ =
If $x,\;y$ and $r$ are positive integers, then $^x{C_r}{ + ^x}{C_{r - 1}}^y{C_1}{ + ^x}{C_{r - 2}}^y{C_2} + .......{ + ^y}{C_r} = $
The number of $4$ letter words (with or without meaning) that can be formed from the eleven letters of the word $'EXAMINATION'$ is
The number of ways of dividing $52$ cards amongst four players equally, are