If $n$ and $r$ are two positive integers such that $n \ge r,$ then $^n{C_{r - 1}}$$ + {\,^n}{C_r} = $
$^n{C_{n - r}}$
$^n{C_r}$
$^{n - 1}{C_r}$
$^{n + 1}{C_r}$
Two packs of $52$ cards are shuffled together. The number of ways in which a man can be dealt $26$ cards so that he does not get two cards of the same suit and same denomination is
$^{20}C_1 + 3 ^{20}C_2 + 3 ^{20}C_3 + ^{20}C_4$ is equal to-
If $n$ is even and the value of $^n{C_r}$ is maximum, then $r = $
Determine the number of $5$ card combinations out of a deck of $52$ cards if there is exactly one ace in each combination.
Ten persons, amongst whom are $A, B$ and $C$ to speak at a function. The number of ways in which it can be done if $A$ wants to speak before $B$ and $B$ wants to speak before $C$ is