MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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9)
![**Permutations and Combinations - Calculating Permutations**
**Evaluate the expression \( ^6P_6 \).**
In permutations, \( ^nP_r \) represents the number of ways to choose \( r \) items from \( n \) items without replacement and where order matters. The formula to calculate a permutation is given by:
\[
^nP_r = \frac{n!}{(n-r)!}
\]
For this particular problem, we have:
\[
^6P_6 = \frac{6!}{(6-6)!}
\]
Calculating the factorials, we have:
- \( 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \)
- \( (6-6)! = 0! = 1 \) (By definition, 0! is equal to 1)
Substitute these values back into the formula:
\[
^6P_6 = \frac{720}{1} = 720
\]
Thus, the value of \( ^6P_6 \) is 720.](https://content.bartleby.com/qna-images/question/a0615f7c-3e91-45ec-8ebd-43a498fc758f/8501881d-19b5-401a-b5b4-6f8c88ec7708/vjn2v2t_processed.jpeg)
Transcribed Image Text:**Permutations and Combinations - Calculating Permutations**
**Evaluate the expression \( ^6P_6 \).**
In permutations, \( ^nP_r \) represents the number of ways to choose \( r \) items from \( n \) items without replacement and where order matters. The formula to calculate a permutation is given by:
\[
^nP_r = \frac{n!}{(n-r)!}
\]
For this particular problem, we have:
\[
^6P_6 = \frac{6!}{(6-6)!}
\]
Calculating the factorials, we have:
- \( 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \)
- \( (6-6)! = 0! = 1 \) (By definition, 0! is equal to 1)
Substitute these values back into the formula:
\[
^6P_6 = \frac{720}{1} = 720
\]
Thus, the value of \( ^6P_6 \) is 720.
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