$A$ committee of $7$ members is to be formed from $9$ boys and $4$ girls. In how many ways can this be done if the committee consists of at most $3$ girls?

Consider a class of $5$ girls and $7$ boys. The number of different teams consisting of $2$ girls and $3$ boys that can be formed from this class,if there are two specific boys $A$ and $B$ who refuse to be members of the same team,is

$_n{P_r} \div \binom{n}{r} = ..........$

The number of ways of distributing $8$ identical rings to $3$ different girls so that every girl gets at least $1$ ring is

Out of $6$ books,in how many ways can a set of one or more books be chosen?

In how many ways can a committee of $5$ members be formed from $4$ gentlemen and $6$ ladies such that the number of gentlemen is greater than the number of ladies?