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?
Because the selection order of committee members is not important.
In this scenario, the focus is on selecting a group of committee members rather than the sequence in which they are chosen. The combination technique is applicable here because it emphasizes the selection of members without regard to the order, which is crucial for forming a committee.
This statement suggests a relationship that does not pertain to the selection method. The combination technique's application is not influenced by attendance records but rather by the need to form a group regardless of who attends meetings.
This choice incorrectly states that the order of selection matters. In committee selection, what is important is the final group composition, not the sequence in which members are selected, which directly contradicts the rationale for using combinations.
While this statement may be true, it does not address the primary reason for using combinations over permutations. The lack of correlation does not justify the choice method; rather, it is the irrelevance of order in selection that necessitates the use of combinations.
In selecting members for the finance committee, the combination technique is ideal as it disregards the order of selection, focusing solely on the group itself. This is essential when the goal is to create a committee of five from nine members, emphasizing that the arrangement does not affect the group’s functionality or decision-making process. Thus, understanding the nature of the selection task is key to applying the correct mathematical technique.
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