The number of $5$ card combinations out of a deck of $52$ cards such that there is exactly one ace in each combination is:

$A$ question paper is divided into two parts,$A$ and $B$,each consisting of $5$ questions. If a candidate has to select $6$ questions in total,in how many ways can they do so if they must select at least $2$ questions from each part?

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?

The number of ways a committee of $8$ members can be formed from a group of $10$ men and $8$ women such that the committee contains at most $5$ men and at least $5$ women is:

Determine $n$ if $^{2n}C_{3} : ^{n}C_{3} = 12 : 1$.

From $5$ consonants and $5$ vowels,how many words can be formed using $3$ consonants and $2$ vowels?