The value of $^{15}{C_3}{ + ^{15}}{C_{13}}$ is
$^{16}{C_3}$
$^{30}{C_{16}}$
$^{15}{C_{10}}$
$^{15}{C_{15}}$
Let the number of elements in sets $A$ and $B$ be five and two respectively. Then the number of subsets of $A \times B$ each having at least $3$ and at most $6$ element is :
$^n{C_r}{ + ^{n - 1}}{C_r} + ......{ + ^r}{C_r}$ =
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 four-letter words that can be formed with letters $a, b, c$ such that all three letters occur is
Out of $6$ books, in how many ways can a set of one or more books be chosen