Question Number 81725 by zainal tanjung last updated on 14/Feb/20
$$\mathrm{If}\:\:\mathrm{7}\:\mathrm{points}\:\mathrm{out}\:\mathrm{of}\:\mathrm{12}\:\mathrm{are}\:\mathrm{in}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{straight}\:\mathrm{line},\:\mathrm{then}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{triangles}\:\mathrm{formed}\:\mathrm{is} \\ $$
Commented by Tony Lin last updated on 14/Feb/20
$${C}_{\mathrm{3}} ^{\mathrm{5}} +{C}_{\mathrm{2}} ^{\mathrm{5}} {C}_{\mathrm{1}} ^{\mathrm{7}} +{C}_{\mathrm{1}} ^{\mathrm{5}} {C}_{\mathrm{2}} ^{\mathrm{7}} =\mathrm{185} \\ $$