$^n{C_r}{ + ^{n - 1}}{C_r} + ......{ + ^r}{C_r}$ =
$^{n + 1}{C_r}$
$^{n + 1}{C_{r + 1}}$
$^{n + 2}{C_r}$
${2^n}$
Let $S=\{1,2,3, \ldots ., 9\}$. For $k=1,2, \ldots \ldots, 5$, let $N_K$ be the number of subsets of $S$, each containing five elements out of which exactly $k$ are odd. Then $N_1+N_2+N_3+N_4+N_5=$
Find the number of ways of selecting $9$ balls from $6$ red balls, $5$ white balls and $5$ blue balls if each selection consists of $3$ balls of each colour.
If $\alpha { = ^m}{C_2}$, then $^\alpha {C_2}$is equal to
If $'n'$ objects are arranged in a row then the number of ways of selecting three of these objects so that no two of them are next to each othe
In how many ways can one select a cricket team of eleven from $17$ players in which only $5$ players can bowl if each cricket team of $11$ must include exactly $4$ bowlers?