Question

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

Answer 1

`_7P_5=(7!)/((7-5)!)=(7!)/(2!)=3\cdot4\cdot5\cdot6\cdot7=2520\\_7C_5=(7!)/(5!2!)=(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.

`(_nP_k)/(_nC_k)=((n!)/((n-k)!))/((n!)/(k!(n-k)!))=(n!)/((n-k)!)\cdot (k!(n-k)!)/(n!)=k!`