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Chapter 8: Problem 62

Describe what \(_{n} P_{r}\) represents.

Short Answer

Expert verified
\(_{n} P_{r}\) represents the number of permutations or ways to arrange \(r\) distinct elements from a set of \(n\) distinct elements. The formula for \(_{n} P_{r}\) is \( \frac{n!}{(n-r)!} \).

Step by step solution

01

Understand what Permutation is

First, it's important to understand what permutation means in combinatorics. Permutation refers to the arrangement of objects in a specific order. It matters where each object is placed. For example, 'ABC' and 'CBA' are two different permutations of the same set of elements.
02

Apply Permutation to the term \(_{n} P_{r}\)

\(_{n} P_{r}\), often read as 'n permute r', is a formula used to calculate the number of permutations or ways to arrange \(r\) distinct elements from a set of \(n\) distinct elements. The order of arrangement is important in permutation.
03

Compute \(_{n} P_{r}\) formula

The formula for \(_{n} P_{r}\) is \( \frac{n!}{(n-r)!} \), where \(n!\) signifies the factorial of \(n\) - the product of all positive integers from 1 to \(n\), and \((n-r)!\) is the factorial of \((n-r)\).

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