What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these are all $4$ cards face cards?

If $^nC_{12} = ^nC_6$,then $^nC_2 = $

If a committee consists of $3$ men and $2$ women,in how many ways can a committee of $5$ members be formed from $5$ men and $4$ women?

$A$ linguistic club of a certain Institute consists of $6$ girls and $4$ boys. $A$ team of $4$ members is to be selected from this group,including the selection of a Captain (from among these $4$ members) for the team. If the team has to include at most one boy,the number of ways of selecting the team is:

$A$ student is asked to answer $10$ out of $13$ questions in an examination such that he must answer at least four questions from the first five questions. Then the total number of possible choices available to him is

If $^{n^2 - n}C_2 = ^{n^2 - n}C_{10}$,then $n = $