Question Number 25786 by gugalesweta@gmail.com last updated on 14/Dec/17 | ||
$$\mathrm{If}\:{C}_{\mathrm{0}} +\:{C}_{\mathrm{1}} +\:{C}_{\mathrm{2}} +...+\:{C}_{{n}} \:=\:\mathrm{256},\:\mathrm{then} \\ $$$$\:^{\mathrm{2}{n}} {C}_{\mathrm{2}} \:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ | ||
Answered by mrW1 last updated on 14/Dec/17 | ||
$${C}_{\mathrm{0}} +{C}_{\mathrm{1}} +...+{C}_{{n}} =\mathrm{2}^{{n}} =\mathrm{256}=\mathrm{2}^{\mathrm{8}} \\ $$$$\Rightarrow{n}=\mathrm{8} \\ $$$${C}_{\mathrm{2}} ^{\mathrm{2}{n}} ={C}_{\mathrm{2}} ^{\mathrm{16}} =\frac{\mathrm{16}×\mathrm{15}}{\mathrm{2}×\mathrm{1}}=\mathrm{120} \\ $$ | ||