If $^n{P_r}$=$ 720$.$^n{C_r},$ then $r$ is equal to
$6$
$5$
$4$
$7$
An urn contains $5$ red marbles, $4$ black marbles and $3$ white marbles. Then the number of ways in which $4$ marbles can be drawn so that at the most three of them are red is
If $^{n} C_{8}=\,^{n} C_{2},$ find $^{n} C_{2}.$
If $^n{C_{12}} = {\,^n}{C_6}$, then $^n{C_2} = $
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
Let $S=\{1,2,3,5,7,10,11\}$. The number of nonempty subsets of $S$ that have the sum of all elements a multiple of $3$ , is $........$