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Question Number 81725 by zainal tanjung last updated on 14/Feb/20

If  7 points out of 12 are in the same  straight line, then the number of  triangles formed is

$$\mathrm{If}\:\:\mathrm{7}\:\mathrm{points}\:\mathrm{out}\:\mathrm{of}\:\mathrm{12}\:\mathrm{are}\:\mathrm{in}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{straight}\:\mathrm{line},\:\mathrm{then}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{triangles}\:\mathrm{formed}\:\mathrm{is} \\ $$

Commented by Tony Lin last updated on 14/Feb/20

C_3 ^5 +C_2 ^5 C_1 ^7 +C_1 ^5 C_2 ^7 =185

$${C}_{\mathrm{3}} ^{\mathrm{5}} +{C}_{\mathrm{2}} ^{\mathrm{5}} {C}_{\mathrm{1}} ^{\mathrm{7}} +{C}_{\mathrm{1}} ^{\mathrm{5}} {C}_{\mathrm{2}} ^{\mathrm{7}} =\mathrm{185} \\ $$

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