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Chapter 11: Problem 60

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

Short Answer

Expert verified
\({ }_{n} P_{r}\) stands for permutations, representing the number of ways of selecting 'r' distinct items from 'n' items in an ordered manner. It can be mathematically represented as \(\frac{n!}{(n-r)!}\). The interpretation of \({ }_{n} P_{r}\) is applicable in situations where the order of arrangement or selection is meaningful.

Step by step solution

01

Understanding notations

In general, in mathematics, the symbol \({ }_{n} P_{r}\) represents the number of ways of obtaining an ordered arrangement of 'r' objects from a larger set of 'n' objects. It is also known as 'Permutations of n elements taken r at a time.'
02

Interpreting Permutations

The concept applies when the order of selection matters. It considers each unique arrangement as a different permutation. For instance, if we have three letters A, B, C and we want to form permutations of 2 letters at a time, then AB and BA are considered two different permutations because the order is different.
03

Mathematical formula

Mathematically, \({ }_{n} P_{r}\) is defined as \(n*(n-1)*(n-2)*...*(n-r+1)\), which could also be represented as \(\frac{n!}{(n-r)!}\) where \(n!\) stands for factorial of n, which multiplies all positive integers up to n. The sign `!' implying factorial means multiplication of descending natural numbers.

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