15. 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: D
Because the selection order of committee members is not important
The combination technique should be used when selecting committee members because the order in which members are selected does not affect the outcome. This makes combinations the appropriate method for determining the group.
A) Because the selection order of committee members is important
This option is incorrect because the selection order is irrelevant when forming a committee. In this scenario, the focus is on selecting a group of five members from the nine available, without regard to the sequence of their selection.
B) Because there is not a correlation between committee member meeting attendance and selection
This option does not pertain to the concept of combinations. While attendance might be a factor in the decision-making process, it does not affect the mathematical approach of selecting committee members, which is purely based on the group composition rather than individual characteristics.
C) Because there is a correlation between committee member meeting attendance and selection
Similar to Option B, this statement is unrelated to the proper use of combinations. While attendance may be relevant for other considerations, it does not influence whether the order of selection matters, which is the key point in using combinations.
D) Because the selection order of committee members is not important
This option is correct as it accurately reflects the fundamental principle of combinations. The definition of combinations highlights that the arrangement of selected individuals does not change the overall group, making this method suitable for forming the finance committee.
Conclusion
The correct answer, D, emphasizes that the order of selection is not significant when choosing members for the finance committee, which aligns perfectly with the concept of combinations. Options A, B, and C fail to address the primary reason for utilizing combinations, which is the lack of importance of selection order in this context. Thus, D is the definitive choice when applying combinatorial principles to committee selection.