Hello! I need some reassurance on the top question please

SOLUTION
[tex]^7P_4[/tex]Therefore,
[tex]\begin{gathered} nPr=\frac{n!}{\left(n-r\right)!}=\frac{7!}{\left(7-4\right)!}=\frac{7!}{3!}=\frac{7\times6\times5\times4\times3!}{3!}=7\times6\times5\times4=840 \\ \end{gathered}[/tex]Hence, the answer is 840 arrangements.