Question Number 28248 by mondodotto@gmail.com last updated on 22/Jan/18
Answered by mrW2 last updated on 22/Jan/18
$$\mathrm{3}×\frac{{n}\left({n}−\mathrm{1}\right)\left({n}−\mathrm{2}\right)}{\mathrm{6}}=\mathrm{7}×\frac{{n}\left({n}−\mathrm{1}\right)}{\mathrm{2}} \\ $$$${n}−\mathrm{2}=\mathrm{7} \\ $$$$\Rightarrow{n}=\mathrm{9} \\ $$$$ \\ $$$${check}: \\ $$$${C}_{\mathrm{3}} ^{\mathrm{9}} =\mathrm{84} \\ $$$${C}_{\mathrm{2}} ^{\mathrm{9}} =\mathrm{36} \\ $$$$\mathrm{3}×\mathrm{84}=\mathrm{252} \\ $$$$\mathrm{7}×\mathrm{36}=\mathrm{252} \\ $$
Commented by mondodotto@gmail.com last updated on 22/Jan/18
$$\mathrm{thanx}\:\mathrm{a}\:\mathrm{lot}\:\mathrm{sir} \\ $$