Answer:
[tex]^8P_4=1680[/tex]
Step-by-step explanation:
Given: [tex]^8P_4[/tex]
Formula:
[tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
It is permutation formula which helps to find number of arrangement.
If we have three digits and to find how many different three digit number be form. We can find using permutation.
Using formula,
[tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
[tex]^8P_4=\dfrac{8!}{(8-4)!}[/tex]
[tex]^8P_4=\dfrac{8!}{4!}[/tex]
[tex]^8P_4=\dfrac{8\times 7\times 6\times 5\times 4!}{4!}[/tex]
Cancel 4! from top and bottom
[tex]^8P_4=8\times 7\times 6\times 5[/tex]
[tex]^8P_4=1680[/tex]
Hence, The value of [tex]^8P_4[/tex] is 1680
