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
What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these
two are red cards and two are black cards,
The number of ways of dividing $52$ cards amongst four players so that three players have $17$ cards each and the fourth player just one card, is
The number of onto functions $f$ from $\{1, 2, 3, …, 20\}$ only $\{1, 2, 3, …, 20\}$ such that $f(k)$ is a multiple of $3$, whenever $k$ is a multiple of $4$, is
In how many ways can $6$ persons be selected from $4$ officers and $8$ constables, if at least one officer is to be included
Number of different words that can be formed from all letters of word $APPLICATION$ such that two vowels never come together is -