In how many ways can a committee be formed of $5$ members from $6$ men and $4$ women if the committee has at least one woman?

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

In an election,the number of candidates is $1$ greater than the persons to be elected. If a voter can vote in $254$ ways,then the number of candidates is:

$A$ man has $7$ friends. In how many ways can he invite one or more of them for a tea party?

An engineer is required to visit a factory for exactly $4$ days during the first $15$ days of every month,and it is mandatory that no two visits take place on consecutive days. The number of all possible ways in which such visits to the factory can be made by the engineer during $1-15$ June $2021$ is:

What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these are two red cards and two black cards?