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 where the order of selection does not affect the outcome. This is a classic situation for using combinations rather than permutations, as the arrangement of chosen members is irrelevant.
This choice is incorrect because if the order were important, permutations would be used instead of combinations. In committee selections like this one, the arrangement of members does not influence the committee's function, making order unimportant.
While attendance might be a factor in other contexts, it does not directly impact the use of combinations here. The choice of committee members relies solely on the selection process, not on their past attendance behaviors, thus making this option irrelevant.
Similar to option B, this statement introduces an unrelated aspect regarding attendance. The selection process for the committee is based on choosing members without regard to their previous attendance, so this correlation does not justify the use of combinations.
This is the correct statement as it emphasizes that the arrangement of selected members has no bearing on the committee's purpose or decisions. The focus is simply on which members are chosen, validating the use of combinations for this selection.
In selecting committee members from a group where order does not matter, using combinations is the appropriate method. The correct rationale highlights the irrelevance of selection order, while the incorrect options either misinterpret the situation or introduce unrelated factors. Understanding this principle aids in making efficient and logical selections in various contexts.
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