select the correct answer.\nthere are 9 applicants for 3 jobs: software engineer, computer programmer, and…

select the correct answer.\nthere are 9 applicants for 3 jobs: software engineer, computer programmer, and systems manager. which statement best describes this situation?\na. there are $_9p_3 = 504$ ways the positions can be filled because the order in which the applicants are chosen doesnt matter.\nb. there are $_9c_3 = 84$ ways the positions can be filled because the order in which the applicants are chosen doesnt matter.\nc. there are $_9p_3 = 504$ ways the positions can be filled because the order in which the applicants are chosen matters.\nd. there are $_9c_3 = 84$ ways the positions can be filled because the order in which the applicants are chosen matters.

select the correct answer.\nthere are 9 applicants for 3 jobs: software engineer, computer programmer, and systems manager. which statement best describes this situation?\na. there are $_9p_3 = 504$ ways the positions can be filled because the order in which the applicants are chosen doesnt matter.\nb. there are $_9c_3 = 84$ ways the positions can be filled because the order in which the applicants are chosen doesnt matter.\nc. there are $_9p_3 = 504$ ways the positions can be filled because the order in which the applicants are chosen matters.\nd. there are $_9c_3 = 84$ ways the positions can be filled because the order in which the applicants are chosen matters.

Answer

Explanation:

Step1: Identify the problem type

This is a permutation - combination problem. Since the jobs (software engineer, computer programmer, and systems manager) are distinct, the order in which the applicants are chosen for the jobs matters.

Step2: Recall the permutation and combination formulas

The formula for permutations is ${n}P{r}=\frac{n!}{(n - r)!}$, and for combinations is ${n}C{r}=\frac{n!}{r!(n - r)!}$, where $n$ is the number of items and $r$ is the number of items to be chosen. Here $n = 9$ (number of applicants) and $r=3$ (number of jobs).

Step3: Calculate the number of permutations

${9}P{3}=\frac{9!}{(9 - 3)!}=\frac{9!}{6!}=\frac{9\times8\times7\times6!}{6!}=9\times8\times7 = 504$.

Answer:

C. There are ${9}P{3}=504$ ways the positions can be filled because the order in which the applicants are chosen matters.