Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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The image contains the mathematical notation for a permutation function.

**Transcription:**
\[ {}^{10}P_{3} \]

**Explanation:**
The notation \({}^{10}P_{3}\) is used in combinatorial mathematics to denote a permutation. Specifically, it represents the number of ways to arrange 10 distinct items into a sequence of length 3. The general formula for permutations is given by:

\[ nP_{r} = \frac{n!}{(n-r)!} \]

For \({}^{10}P_{3}\):

\[ {}^{10}P_{3} = \frac{10!}{(10-3)!} = \frac{10!}{7!} \]

Where \( n! \) (n factorial) is the product of all positive integers up to \( n \).

In simpler terms, the expression \({}^{10}P_{3}\) tells us how many different ways we can arrange 3 items out of a total of 10 distinct items.
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Transcribed Image Text:The image contains the mathematical notation for a permutation function. **Transcription:** \[ {}^{10}P_{3} \] **Explanation:** The notation \({}^{10}P_{3}\) is used in combinatorial mathematics to denote a permutation. Specifically, it represents the number of ways to arrange 10 distinct items into a sequence of length 3. The general formula for permutations is given by: \[ nP_{r} = \frac{n!}{(n-r)!} \] For \({}^{10}P_{3}\): \[ {}^{10}P_{3} = \frac{10!}{(10-3)!} = \frac{10!}{7!} \] Where \( n! \) (n factorial) is the product of all positive integers up to \( n \). In simpler terms, the expression \({}^{10}P_{3}\) tells us how many different ways we can arrange 3 items out of a total of 10 distinct items.
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