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Consider the Following Formulas Given the Same Values for N and R in Each

question 45

Essay

Consider the following formulas: nPr=n!(nr)! and nr=n!(nr)!r!{ } _ { n } \mathrm { P } _ { \mathrm { r } } = \frac { \mathrm { n } ! } { ( \mathrm { n } - \mathrm { r } ) ! } \text { and } \mathrm { n } _ { \mathrm { r } } = \frac { \mathrm { n } ! } { ( \mathrm { n } - \mathrm { r } ) ! \mathrm { r } ! } Given the same values for n and r in each formula, which is the smaller value, P or C? How does this relate to the concept of counting the number of outcomes based on whether or not order is a criterion?

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Definitions:

Generalize

To draw a broad conclusion from specific instances, allowing for the application of findings in a general context.

Correlation

A statistical measure that describes the extent to which two variables change together.

Variables

Elements, features, or factors that are liable to vary or change within a study or experiment.

Representative Sample

A smaller group taken from a larger population that accurately represents the characteristics of the whole population.

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