The value of $\sum\limits_{r = 0}^{n - 1} {\frac{{^n{C_r}}}{{^n{C_r} + {\,^n}{C_{r + 1}}}}} $ equals
$n + 1$
$\frac{n}{2}$
$n + 2$
None of these
In how many ways can a committee be formed of $5$ members from $6$ men and $4$ women if the committee has at least one woman
Out of $6$ books, in how many ways can a set of one or more books be chosen
$^n{C_r}{ + ^{n - 1}}{C_r} + ......{ + ^r}{C_r}$ =
In how many ways can the letters of the word $\mathrm{ASSASSINATION} $ be arranged so that all the $\mathrm{S}$ 's are together?
In the $13$ cricket players $4$ are bowlers, then how many ways can form a cricket team of $11$ players in which at least $2$ bowlers included