From among the $36$ teachers in a school,one principal and one vice-principal are to be appointed. In how many ways can this be done?

In an election,there are $5$ candidates and $3$ vacancies. $A$ voter can vote for a maximum of $3$ candidates. In how many ways can a voter cast their vote?

Given six line segments of lengths $2, 3, 4, 5, 6, 7$ units,the number of triangles that can be formed by these lines is

Total number of four-digit odd numbers that can be formed using $0, 1, 2, 3, 5, 7$ (repetition allowed) are

If $\alpha = {^m}{C_2}$,then ${^\alpha}{C_2}$ is equal to

$A$ 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?