Given the Same Values for N and R in Each

question 51

Essay

$\text { Consider the following formulas: } ( n ) _ { r } = \frac { n ! } { ( n - r ) ! } \text { and } \left( \begin{array} { l } n \\ r \end{array} \right) = \frac { n ! } { ( n - r ) ! r ! } \text {. }$
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:

Mammals

A class of warm-blooded vertebrate animals that have, in the female, milk-secreting organs for feeding the young.

Compound Proposition

A statement formed by combining two or more propositions using logical connectives such as "and," "or," "if...then."

Asserted

Stated positively or affirmed with confidence.

Sentence Expresses

Conveys or represents the meaning or thought that someone wishes to communicate through words arranged logically.