Question

Which is greater, 7 P 5 or 7 C 5? 7P5 7C5

Answer 1

$_7P_5=\dfrac{7!}{(7-5)!}=\dfrac{7!}{2!}=3\cdot4\cdot5\cdot6\cdot7=2520\\_7C_5=\dfrac{7!}{5!2!}=\dfrac{6\cdot7}{2}=21\\\\\\_7P_5> {_7C_5}$

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$_nP_k$ is always greater than $_nC_k$. And it's greater $k!$ times.

$\dfrac{_nP_k}{_nC_k}=\dfrac{\dfrac{n!}{(n-k)!}}{\dfrac{n!}{k!(n-k)!}}=\dfrac{n!}{(n-k)!}\cdot \dfrac{k!(n-k)!}{n!}=k!$