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Evaluate the expression Pg. sPs =O

Evaluate the expression Pg. sPs =O

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Exercise: Evaluating Permutations** Consider the following expression: \( ^5P_5 \). ### Task Evaluate the expression \( ^5P_5 \). ### Solution: The expression \( ^nP_r \) represents the number of permutations of \( n \) items taken \( r \) at a time, and it is calculated using the formula: \[ ^nP_r = \frac{n!}{(n-r)!} \] For \( ^5P_5 \): 1. \( n = 5 \) and \( r = 5 \). 2. Substitute these into the formula: \[ ^5P_5 = \frac{5!}{(5-5)!} = \frac{5!}{0!} \] 3. We know that \( 0! = 1 \), so: \[ ^5P_5 = \frac{5!}{1} = 5! \] 4. Calculate \( 5! \): \[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \] ### Conclusion Therefore, \( ^5P_5 = 120 \). This exercise helps in understanding how to evaluate permutations using factorials. Permutations are useful in scenarios where the order of selection matters.
Transcribed Image Text:**Exercise: Evaluating Permutations** Consider the following expression: \( ^5P_5 \). ### Task Evaluate the expression \( ^5P_5 \). ### Solution: The expression \( ^nP_r \) represents the number of permutations of \( n \) items taken \( r \) at a time, and it is calculated using the formula: \[ ^nP_r = \frac{n!}{(n-r)!} \] For \( ^5P_5 \): 1. \( n = 5 \) and \( r = 5 \). 2. Substitute these into the formula: \[ ^5P_5 = \frac{5!}{(5-5)!} = \frac{5!}{0!} \] 3. We know that \( 0! = 1 \), so: \[ ^5P_5 = \frac{5!}{1} = 5! \] 4. Calculate \( 5! \): \[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \] ### Conclusion Therefore, \( ^5P_5 = 120 \). This exercise helps in understanding how to evaluate permutations using factorials. Permutations are useful in scenarios where the order of selection matters.
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Step 1

Farmula

nPr=n!/(n-r)!

And n!=n(n-1)(n-2).....3.2.1

 

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