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

The number of ways of distributing $500$ dissimilar boxes equally among $50$ persons is:

In an election,the number of candidates is $1$ more than the number of persons to be elected. If the voters can cast their votes in $254$ ways,find the number of candidates. ($A$ voter cannot cast more votes than the number of persons to be elected.)

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

$A$ 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 must consist of exactly $3$ girls?

Out of $10$ white,$9$ black and $7$ red balls,the number of ways in which selection of one or more balls can be made,is