$A$ committee of $5$ is to be formed out of $6$ men and $4$ ladies. The number of ways this can be done,when at most $2$ ladies are included,is

$A$ student is allowed to select at most $n$ books from a collection of $(2n + 1)$ books. If the total number of ways in which he can select at least one book is $63$,then the value of $n$ is

If $\binom{n}{3} + \binom{n}{4} > \binom{n+1}{3}$,then:

The solution set of $^{10}C_{x-1} > 2 \cdot ^{10}C_x$ is

If $^{20}C_{n+2} = ^nC_{16}$,then the value of $n$ is

What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these do the four cards belong to four different suits?