[tex]_7P_5=\dfrac{7!}{(7-5)!}=\dfrac{7!}{2!}=3\cdot4\cdot5\cdot6\cdot7=2520\\_7C_5=\dfrac{7!}{5!2!}=\dfrac{6\cdot7}{2}=21\\\\\\_7P_5> {_7C_5}[/tex]
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[tex]_nP_k[/tex] is always greater than [tex]_nC_k[/tex]. And it's greater [tex]k![/tex] times.
[tex]\dfrac{_nP_k}{_nC_k}=\dfrac{\dfrac{n!}{(n-k)!}}{\dfrac{n!}{k!(n-k)!}}=\dfrac{n!}{(n-k)!}\cdot \dfrac{k!(n-k)!}{n!}=k![/tex]
