In how many ways can $6$ persons be selected from $4$ officers and $8$ constables,if at least one officer is to be included?

The number of ways of dividing $52$ cards amongst four players so that three players have $17$ cards each and the fourth player has just one card,is

Out of $7$ consonants and $4$ vowels,how many words of $3$ consonants and $2$ vowels can be formed?

$A$ question paper is divided into two parts $A$ and $B$,and each part contains $5$ questions. The number of ways in which a candidate can answer $6$ questions by selecting at least two questions from each part is:

$A$ box contains two white balls,three black balls,and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?

In how many ways,a committee of $3$ members can be selected from $5$ men and $4$ women,consisting of $2$ men and $1$ woman?