Here are the essential concepts you must grasp in order to answer the question correctly.
Combinations
Combinations refer to the selection of items from a larger set where the order of selection does not matter. The notation 'nCr' or 'C(n, r)' represents the number of ways to choose 'r' items from 'n' items. This concept is crucial in probability and statistics, especially when determining possible outcomes in scenarios where arrangement is irrelevant.
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Factorial
A factorial, denoted as 'n!', is the product of all positive integers up to 'n'. It is used in combinations and permutations to calculate the total arrangements of a set. For example, 5! equals 5 × 4 × 3 × 2 × 1 = 120. Understanding factorials is essential for performing calculations involving combinations and permutations.
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Binomial Coefficient
The binomial coefficient, often represented as 'C(n, r)' or 'nCr', quantifies the number of ways to choose 'r' elements from a set of 'n' elements without regard to the order of selection. It is calculated using the formula C(n, r) = n! / (r!(n-r)!), which incorporates factorials. This concept is fundamental in combinatorial mathematics and probability theory.
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Coefficient of Determination
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