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If-m-C-1-n-C-2-express-m-in-terms-of-n-

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Question Number 114943 by ZiYangLee last updated on 22/Sep/20
If ^m C_1 =^n C_2 , express m in terms of n.
$$\mathrm{If}\:\:^{{m}} {C}_{\mathrm{1}} =\:^{{n}} {C}_{\mathrm{2}} \:, \\ $$$$\mathrm{express}\:{m}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{n}. \\ $$
Answered by Dwaipayan Shikari last updated on 22/Sep/20
((m!)/(1!(m−1)!))=((n!)/(2!(n−2)!)) m=((n(n−1))/2)
$$\frac{{m}!}{\mathrm{1}!\left({m}−\mathrm{1}\right)!}=\frac{{n}!}{\mathrm{2}!\left({n}−\mathrm{2}\right)!} \\ $$$${m}=\frac{{n}\left({n}−\mathrm{1}\right)}{\mathrm{2}} \\ $$
Commented by ZiYangLee last updated on 26/Sep/20
Tks
$$\mathrm{Tks} \\ $$

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