Given the permutation expression, [tex]^8P_5[/tex], the value of the expression is: 6,720.
Recall:
- In Permutation, order matters and the following general rule is given: [tex]^nP_r = \frac{n!}{(n - r)!}[/tex]
Given the expression: [tex]^8P_5[/tex], the following shows how to evaluate the expression by applying the general case formula for Permutation.
Thus:
Where,
8 = 5
r = 5
[tex]^8P_5 = \frac{8!}{(8 - 5)!}\\\\^8P_5 = \frac{8!}{3!}\\\\^8P_5 = \frac{8 \times 7 \times 6 \times 5 \times 4 \times 3!}{3!} \\\\^8P_5 = 8 \times 7 \times 6 \times 5 \times 4\\\\\mathbf{^8P_5 = 6,720}[/tex]
Therefore, given the permutation expression, [tex]^8P_5[/tex], the value of the expression is: 6,720.
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