9. A school board has nine voting members. Five members need to be chosen each year for the finance committee. Why should the combination technique be used when selecting committee members?

Answer: C

Explanation:

Because the selection order of committee members is not important

Using the combination technique is appropriate in this context because the order in which committee members are selected does not affect the outcome of the selection process.

A) Because there is a correlation between committee member meeting attendance and selection

This option is incorrect because the correlation between meeting attendance and selection has no relevance to the selection order of committee members. The selection process is concerned with choosing members, not their attendance records.

B) Because the selection order of committee members is important

This option is incorrect as it contradicts the fundamental principle of combinations. In this scenario, the order of selection is irrelevant; only the members chosen matter, which supports the use of combinations rather than permutations.

C) Because the selection order of committee members is not important

This option is correct because it highlights the essence of using combinations. The selection process focuses on the group of members chosen for the finance committee, not the sequence in which they are selected, making combinations the appropriate method.

D) Because there is not a correlation between committee member meeting attendance and selection

While this statement may be true, it does not address the core reason for using combinations in the selection process. The lack of correlation does not determine the importance of order in selecting committee members.

Conclusion

The correct answer is C, as it directly addresses the key reason for using combinations: the selection order does not affect the outcome. Options A and B misinterpret the relevance of selection order, while D fails to connect directly to the combination technique's rationale. Thus, C is definitively the right choice as it aligns with the principles of combinatorial selection.