Evaluate the expression 6P6. 6P6 =O

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Question
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.
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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