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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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