Question

12 jobseekers applied for 3 available vacant positions in a company. In how many ways can the job be offered among these applicants if a particular applicant must be employed?

Answer 1

As one particular appicant must be employed, we have to count the number of the ways can the 2 available positions be offered to 11 jobseekers. As the order of applicants does not matter, we'll count the number of combinations without repetition:

$N=\begin{pmatrix} 11 \\ 2\end{pmatrix}=\\ =\cfrac{11! } {2! \cdot(11-2)! }=\\ =\cfrac{10\cdot11}{2}=55.$