Question

select the correct answer.
there are 9 applicants for 3 jobs: software engineer, computer programmer, and systems manager. which statement best describes this situation?
a. there are ( _9p_3 = 504 ) ways the positions can be filled because the order in which the applicants are chosen doesnt matter.
b. there are ( _9c_3 = 84 ) ways the positions can be filled because the order in which the applicants are chosen doesnt matter.
c. there are ( _9p_3 = 504 ) ways the positions can be filled because the order in which the applicants are chosen matters.
d. there are ( _9c_3 = 84 ) ways the positions can be filled because the order in which the applicants are chosen matters.

Explanation:

Step1: Identify order relevance

The jobs (software engineer, computer programmer, systems manager) are distinct, so assigning different applicants to different roles means order of selection matters. This is a permutation problem.

Step2: Calculate permutation

The formula for permutations is $_nP_r = \frac{n!}{(n-r)!}$. Here $n=9$, $r=3$.
$$_9P_3 = \frac{9!}{(9-3)!} = \frac{9\times8\times7\times6!}{6!} = 9\times8\times7 = 504$$

Step3: Evaluate options

Option C correctly states permutation is used (order matters) and gives the correct value.

Answer:

C. There are $_9P_3 = 504$ ways the positions can be filled because the order in which the applicants are chosen matters.