Answer to Question #309987 in Statistics and Probability for diamond

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

Fix a particular applicant. There are $3$ positions for him, then there are $11$ applicants for the $2$ remaining positions:

$N=3\cdot C_{11}^2=165$