Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What does "n!/(n-r)!" represent in permutations?

The number of ways to choose r from n
The number of ways to arrange n items
The number of ways to arrange r items from n
The number of combinations of n items

The correct answer is: The number of ways to arrange r items from n

The expression "n!/(n-r)!" is specifically used to calculate the number of permutations of r items selected from a total of n distinct items. This occurs because "n!" calculates the total arrangements (or permutations) of n items, and "(n-r)!" accounts for the arrangements of the items that are not included in the selection of r. By dividing the total arrangements by the arrangements of the items not selected, you isolate the number of ways to arrange the chosen r items. When looking at this in the context of permutations, it's clear that the focus is on the ordered arrangement of the selected items. Therefore, this formula is pivotal in determining how many distinct ways you can pick and arrange r items from a larger set of n items, illustrating its role in the concept of permutations. The other options relate to combinations or choices without regard for order, which is why they do not apply in this context.