Previous in Permutation and Combination Next in Permutation and Combination
Question Number 87731 by mathocean1 last updated on 05/Apr/20
$$\mathrm{solve}\:\mathrm{in}\:\mathbb{N} \\ $$$$\mathrm{A}_{\mathrm{n}} ^{\mathrm{4}} =\mathrm{A}_{\mathrm{n}} ^{\mathrm{3}} \\ $$
Commented by Tony Lin last updated on 06/Apr/20
$${n}\left({n}−\mathrm{1}\right)\left({n}−\mathrm{2}\right)\left({n}−\mathrm{3}\right)={n}\left({n}−\mathrm{1}\right)\left({n}−\mathrm{2}\right) \\ $$$${n}\left({n}−\mathrm{1}\right)\left({n}−\mathrm{2}\right)\left({n}−\mathrm{4}\right)=\mathrm{0} \\ $$$$\because\:{n}\geqslant\mathrm{4} \\ $$$$\therefore{n}=\mathrm{4} \\ $$