$\sum\limits_{r = 0}^m {^{n + r}{C_n} = } $
$^{n + m + 1}{C_{n + 1}}$
$^{n + m + 2}{C_n}$
$^{n + m + 3}{C_{n - 1}}$
None of these
The number of four lettered words that can be formed from the letters of word '$MAYANK$' such that both $A$'s come but never together, is equal to
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 $...........$.
If $^{20}{C_{n + 2}}{ = ^n}{C_{16}}$, then the value of $n$ is
If $^n{C_r}$ denotes the number of combinations of $n$ things taken $r$ at a time, then the expression $^n{C_{r + 1}} + {\,^n}{C_{r - 1}} + \,2 \times {\,^n}{C_r}$ 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